Alright folks, we're in the home stretch now! (Okay, I know the illusionist list is still to come. Don't discourage me.)
There are 24 magic-user spells of 5th level in AD&D. In OD&D there were sixteen, all of which have made the transition at the same level. Of the remaining eight spells, all of them are new except for stone shape, which is new for magic-users but has appeared in the PHB before as a druid spell.
Airy Water: Creates a sphere around the caster that turns water (and "water based infusions or solutions") into a less dense substance that is breathable. It can also be formed as a hemisphere, in which case its diameter is doubled. It also affects movement, allowing creatures within to move unhindered by water. Water-breathers can't survive within the sphere, and those with no movement other than swimming can't move while inside it. Note that the duration of the spell is 1 turn/level: it's good for short-term exploration, but not for long underwater expeditions. Its material component is a handful of alkaline or bromine salts.
Animal Growth: Formerly known as growth/animal, this spell works much like the 5th-level druid spell of the same name. It affects up to 8 animals within the spell area, doubling their Hit Dice and damage. It has a range of 6" (druids have 8"), a duration of 1 rounds/level (for druids it's 2 rounds/level), and a casting time of 5 segments (it takes druids 7 segments). The material component is a pinch of powdered bone.
The OD&D version of the spell affected 1-6 animals, with a "proportionate" raise in attack capabilities. As is often the case with OD&D, the specifics were vague. It had a duration of 12 turns and range of 12".
Animate Dead: Works much like the 3rd-level cleric spell, in that it creates a skeleton or a zombie from the corpse of a dead human. The caster can create a number of undead whose Hit Dice is equal to their level. The material component is a drop of blood, a piece of human flesh, and some bone (either powdered or a shard). The cleric spell was viable for combat use, with a casting time of 1 round, but for magic-users it takes 5 rounds, which kind of limits it to non-combat situations.
In OD&D, the caster could raise 1d6 undead for every caster level above 8th.
Bigby's Interposing Hand: Creates a disembodied hand that places itself between the caster and the target for the whole duration of the spell. The size of the hand can range from that of a human to that of a titan. The hand can be destroyed by normal means, and has as many hit points as the caster. Creatures can try to push past it, and any that weigh less than 2,000 pounds will be slowed to half normal movement. (I wonder what happens when they push the hand right back to the caster? Can they then attack, or does it still block them? Can they push it back past the caster?) The material component is a glove.
This is the introduction of Bigby, who started life as an NPC ran by Rob Kuntz. He was placed under a charm spell by Gary Gygax's PC Mordenkainen, and eventually became loyal enough that Kuntz allowed Gygax to use Bigby as his own PC. He goes on to become a powerful archmage in TSR's official Greyhawk material, but I'm not too familiar with that stuff. As with most of these characters, I'll be trying my best to square the history as laid out by TSR with the anecdotes we have from Gygax and co.
Cloudkill: Creates a cloud of yellowish-green gas (about 4" wide and 2" deep) that moves away from the caster at a rate of 1" per round. Any creature of less than 4+1 Hit Dice caught within the cloud will be instantly killed. Those of 4+1 to 5+1 Hit Dice get a save vs. poison with a -4 penalty, those of up to 6 Hit Dice get a save at no penalty. Presumably those of over 6 Hit Dice are unaffected. Winds can alter the course of the cloud (though they can't push it back towards the caster) and a strong wind will break it up in 4 rounds. Any wind stronger than that makes the spell unusable. Passing through thick vegetation will break it up in 2 rounds. The cloud sinks to the lowest level of the ground, so it can be used to flush out dens and sinkholes (with an ant nest being the given example).
The OD&D spell was deadly to all creatures with less than 5 Hit Dice, and moved at a rate of 6" per turn. (This could be faster or slower than in AD&D, depending on how you interpret the OD&D usage of turns.) The cloud had a 3" diameter (circular, rather than AD&D's more rectangular shape) and lasted for 6 turns (as opposed to 1 round/level in AD&D). It was dispelled by strong winds and trees, but with no time frame given.
Conjure Elemental: Allows the caster to summon an elemental. The type of elemental must be decided when the spell is memorised: air, fire, earth or water. A large fire is needed to summon a fire elemental, and a large body of water for a water elemental. (Presumably the same applies for air and earth elementals, but those are common enough that it wasn't called out in the spell description.) The elemental conjured has 16 Hit Dice, but will only do the caster's bidding so long as the caster fully concentrates on it. As soon as that concentration drops (which can happen when the caster is grappled or wounded) the elemental will attack its summoner (though it will finish whatever combat it's involved in first). Even if the caster maintains concentration, there's a 5% chance every round that the elemental will break free. The caster can protect himself with a pentacle, pentagram, thaumaturgic triangle, magic circle, or a protection from evil spell, but the rules for those are in the DMG (except for the spell). The material components are burning incense for an air elemental; soft clay for earth; sulphur and phosphorus for fire; and water and sand for a water elemental.
The OD&D spell was much the same, but as usual it doesn't get as specific. The main difference is that casters were restricted to one elemental of each type per day. That restriction is hinted at in AD&D ("it is possible to conjure up successive elementals of different type if the spell caster has memorised two or more of these spells"), but it's never stated in concrete fashion. The spell had a range of 24" (as opposed to 6" in AD&D).
Cone of Cold: Here we see yet another offensive staple of the magic-user list making its debut much later in the game's history than expected. It creates a cone that originates from the caster, and extends 1/2" per level, dealing 1d4+1 damage per level. It's interesting that it's not actually a cone of frost, or an icy blast or whatever; the spell is said to "drain heat", so there may be no visual element to it at all. Its material component is a small cone of glass or crystal.
Contact Other Plane: The caster can send their mind to another plane, to contact whatever power lives there for information (one question per 2 caster levels). The power contacted is at random, and will resent the intrusion and give short, probably one-word answers (kind of like me being cold-called by a telemarketer). The caster chooses how far removed from the material plane he wants to go: the further you go, the better the chance that the being contacted will know the answer, but it comes with a higher chance of being lied to, and/or driven insane. You can also contact an Elemental Plane, which has a high likelihood of knowledge and a relatively low chance of being driven insane, but it seems that it can only work for questions pertaining to that element. Characters with a high Int have their chance of being driven insane reduced. Insanity lasts for 1 week for each plane removed from the material (to a maximum of 10), and there's a 1% chance per plane removed that they'll die outright (although this can be stopped with a remove curse).
It's not made clear how this all meshes with the AD&D "Great Wheel" cosmology, but it does make sense in a way. Most of the Outer Planes have levels, but the deepest "good" plane has seven, whereas Hell has nine, and the Abyss has 666. So the deeper you choose to delve, the more likely it is that the power contacted is going to be something really nasty, and more likely to lie or drive you mad.
In OD&D the spell was called Contact Higher Plane, possibly because it was created before the make-up of the planes was properly hammered out. It only permitted answers of "yes" or "no", whereas AD&D allows other one-word answers. The number of questions alloweed was determined by the depth of the plane contacted rather then caster level. In general, the likelihood of knowledge in OD&D was lower than that in AD&D, the chance of being lied to was higher, and the chance of being driven insane was also higher. The chance of being driven insane was lessened by being high level, rather than having a high Intelligence. The planes were numbered 3rd through 12th, and the Elemental Plane could not be contacted (in AD&D, the planes begin as "1 removed" and go to "9 or more removed").
Distance Distortion: Bear with me, because I'm not entirely sure what this spell does. You need to cast it in conjunction with a summoned earth elemental, I get that. The elemental doesn't react with hostility when the spell is cast, which gets around the need to concentrate (which would normally be broken by spell-casting). The spell affects an area of 100" square per level, and any dimensions within that area can be effectively halved or doubled for the length of the spell. The example given is a 100' long corridor being made to seem as if it's 50' long, or 200' long. (It affects the width as well.) What I don't get is whether it's an illusion or not. Are the distances physically altered? Or is it in the minds of those who pass through? The spell's in the Alteration school, so it's probably the former. Either way, it's odd for a spell to require an elemental to function; I can't think of any other spell in the PHB with such a specific dependency. A true seeing spell will reveal the elemental. The material component is a small lump of clay.
Extension II: Prolongs the duration of a spell of 1st-4th level by 50%. I wonder if this really required another spell to accomplish, or if it would have been better served to allow extension I to scale upwards with caster level. (I guess you could say the same thing about monster summoning as well.)
Feeblemind: Works like the 6th-level druid spell, in that it reduces a single spell-caster's intelligence to that of a "moronic child". This can be restored with a heal, restoration or wish. Clerics get a save bonus against the spell, while magic-users and illusionists get a penalty. Non-human magic-users have a lesser penalty than humans. The range for the magic-user spell is 1"/level (it's 16" for druids). and the casting time is 5 segments (druids take 8). The material component is a handful of spheres made out of clay, crystal, glass or minerals.
In OD&D, the spell only worked against magic-users, but it could be fixed with a dispel magic. It had a range of 24".
Hold Monster: Immobilises 1-4 creatures, with the spell being more difficult to save against the less creatures targeted. It's only advantage over hold person is that it can paralyse creatures of any type. I'm not sure what this line means: "partially negated hold monster spell effects equal those of a slow spell". Is there anything in the AD&D rules about saving throws and "partial negation"? It's a mystery to me. The material component is a hard metal rod for each target.
The OD&D spell worked the same, but the save penalty for targeting one creature was -2 rather than -3 (and there was no penalty for targeting 2 or 3 creatures). The duration was 6 turns + caster level (it's 1 round/level in AD&D), and the range was 12" (it's 0.5"/level in AD&D).
Leomund's Secret Chest: This spell requires an expensive chest (not less than 5,000 gp) with some pretty specific material requirements: a wooden chest must have platinum corner fittings, etc.; an ivory chest must have gold fittings; a chest made of bronze, copper or silver must have electrum or silver fittings. A miniature replica of the chest is also needed, and no magic-user may have more than one of these chests (a restriction that can't even be broken with a wish).
The chest can then be hidden in the Ethereal Plane, and is completely undetectable to creatures on the Prime Material Plane. It works a bit like a bag of holding, in that it can hold one cubic foot of material per caster level. Living creatures placed inside are 75% likely to make the spell fail, though, so it's a little harder to stuff an enemy in there and shunt him off to the Ethereal Plane. The caster can summon the chest as long as he has the miniature replica, but if that's lost there's no way to get the chest back.
For every week that the chest spends in the Ethereal Plane, there's a 1% cumulative chance that some extraplanar creature will find it. The creature might ignore it, put something in there, exchange an item, steal an item, or just take the whole lot. Not only that, but whenever the chest is summoned back to the material plane a window is left open for the next 5 hours, with a chance that some creature might be drawn through. Also, if the chest is left in the Ethereal Plane past the spell's duration (60 days), there's a 5% cumulative chance per day that it will be lost forever. Obviously, with the many drawbacks, this is a spell for short-term use only. In the long term, you stuff will be safer somewhere on the Material Plane. (I do wonder about said extraplanar creature's ability to open the chest, though. Does it just automatically bypass locks and traps?)
Magic Jar: The caster transfers their life force to a receptacle of some sort (usually a gem or crystal). From there, the spirit can possess any creature that comes within range. While in the gem, it can sense nearby life forces, but won't know exactly what type of creature they are. While in possession of a creature, the caster has access to the creature's "rudimentary knowledge", but not to specific things like languages and spells. (What this rudimentary knowledge is, I have no idea. Memories? Anything that doesn't pertain to class abilities and the like?) If it's a humanoid form, the caster is able to use their own spell-casting abilities. Possession attempts take 1 round, and the target gets a saving throw (which is modified up or down by comparing the combined Intelligence and Wisdom of the caster and the target). This also determines how often the target gets a saving throw to cast the spirit out: once per round for targets far more mentally powerful than the caster, all the way to once per week for those much mentally weaker. Once the creature regains control, the caster is trapped within it until it can either escape back to the jar or reassert control. Destruction of the caster's original body does no harm to the spirit in the magic jar, but destruction of the jar destroys the spirit utterly.
In OD&D, the magic jar could be any inanimate object, even a simple rock. Otherwise it's much the same, but with nothing said about what knowledge the caster gleans from its target, or whether spells can be used in the new form. None of the rules pertaining to the comparison of combined Intelligence and Wisdom were present, either. The spell had a range of 12", whereas in AD&D it's 1" per level.
Monster Summoning III: Much like monster summoning II and III, summoning 1-4 third-level monsters. Let's once again (remembering that the DMG was not yet published) look at the tables from OD&D to see what sort of monsters we're talking about. (In previous entries I've been consulting the tables in the original three booklets, but I probably should have been looking at the ones in Supplement I: Greyhawk. I'll do that from now on.) Most of the entries are for classed NPCs and some giant animals, but there are also wights, harpies, wererats, and ochre jellies.
The OD&D spell only summoned 1 or 2 creatures.
Mordenkainen's Faithful Hound: Summons a "phantom watchdog" that can only be seen by the caster, and can be set as a guardian. If any creature larger than a cat approaches the area, the hound will start barking. It can detect pretty much anything, even creatures that are ethereal, astral, or invisible. If the intruding creature exposes its back to the hound, it will attack as a 10 Hit Dice creature for 3-18 damage, and can hit creatures normally only struck by magical weapons. The hound can't be attacked, but it can be dispelled. The caster has to remain within 3"of the area to be guarded at all times, or the spell vanishes (which really limits its usefulness, I have to say). I do wonder, can a potential intruder simply get past the hound by never turning their back? I suppose it's hard when the dog's invisible, but it is possible. The material component is a silver whistle, a piece of bone, and a thread.
This is the first appearance of Mordenkainen, Gary's primary PC in the early days, who he apparently advanced to well past level 20. Later TSR material places him as the most powerful archmage in the World of Greyhawk, and a force for balance as the leader of the Circle of Eight. As always, this will need to be reconciled with Gary's various anecdotes.
Passwall: Creates a tunnel 5' wide, 8' high and 10' deep through wooden, plaster or stone walls. Longer tunnels can be created with separate castings of the spell. Its material component is a pinch of sesame seed. (I'm sure Gary had something in mind for most of these components, but some of them are a real mystery.)
The OD&D spell only specified a length (10'). It had a duration of 3 turns (6 turns + 1/level in AD&D), and a range of 3" (unchanged).
Stone Shape: Allows the caster to reshape stone into any form, with a volume of one cubic foot per level. Anything can be created, but fine details aren't possible. It's permanent though, so whatever is made will last forever (or at least until dispelled). The material component is a lump of soft clay, which the caster must shape into the form desired.
The druid version of the spell could affect 3 cubic feet, plus 1 cubic foot per level, so it was slightly more effective. It also needed mistletoe as a component in addition to the clay.
Telekinesis: The caster can move objects at a distance with the power of his mind. The speed of this movement starts at 2" in the first round, then doubles every round until it hits the maximum of 1,024" per round. Doing some math here, we're talking 10,240 feet per minute, or roughly 116 miles per hour. The weight limit is 250gp per level (about 25 pounds), with no cap, but even at mid-levels something travelling at that speed should do some serious damage. (And I'm wondering, is this converted to yards per minute outside? That would give a top speed of just under 350 miles per hour, unless I've spectacularly botched my math.) The spell can be used to push around living creatures, but any sort of walking will negate it as long as the speed isn't up to 16" per round. It can be stopped with an enlarge spell (provided this brings the creature above the maximum weight), by any of the Bigby's Hand spells, or by "many other magics" unspecified in the PHB.
In OD&D, the weight limit was 200gp per level. It had a duration of 6 turns (2 rounds +1/level in AD&D) and a range of 12" (1"/level in AD&D). There was nothing in OD&D about speed of movement, using the spell on living creatures, or ways to negate it.
Teleport: The caster can teleport to any destination, so long as the travel is not interplanar. The amount of weight teleported is equal to 2,500gp, plus 1,500gp per level. For every teleport there's a chance for error, with the likelihood being reduced the more familiar the caster is with the destination. This error could be coming in high (10" above the destination per % roll under the safe range), which is probably not so bad. Coming in low is probably deadly, because materialising in a solid object is instantly fatal. For example, there's only a 1% chance of coming in low for areas the caster is very familiar with, but for an area they've never seen before the chance is up to 15%. Regardless of familiarity, every single teleport comes with a risk. Apparently the area teleported to must have a substantial area of surface, such as a wooden floor, stone floor, or natural ground; there's no designating your destination as 20 feet in the air.
The OD&D spell was even deadlier, with teleportation to an unknown area being 75% likely to result in death. The spell was otherwise the same, but with less detail in terms of how familiar the caster is with the destination (OD&D had three categories, whereas AD&D has five).
Transmute Rock to Mud: Works just like the 5th-level druid spell, in that it turns natural stone into mud. Creatures unable to free themselves from the mud sink and suffocate (with no timeframe or guidelines given). The mud is permanent until dispelled, or until it dries up naturally. It can be reversed as transmute mud to rock. It has a range of 1"/level (as opposed to 16" for druids) and a casting time of 5 segments (7 segment for druids). The material components are clay and water (or sand, lime and water for the reverse).
The OD&D spell could affect sand and earth (which is perhaps possible in AD&D as well, it's open to interpretation), and affects an area of 30" square. Creatures could be trapped in it, but there was nothing said about suffocation. Evaporation took 3-18 days, whereas in AD&D it takes 1-6 days per cubic inch.
Wall of Force: Creates a wall of force that is impervious to pretty much anything except a disintegrate spell. It can be shaped into a globe around the caster, but the caster's spell's can't pass through it. Once created, the wall can't be moved. Its material component is a pinch of powdered diamond.
Wall of Iron: Creates a vertical iron wall that's 15 square feet per level in area, and a quarter-inch thick per level. (That's a real inch, not a game inch.) It can be used to seal up a breached wall or block a tunnel, but if it's not supported it will tip over and crush anything beneath it. (No guidelines for how much damage this does.) It's permanent unless hit with dispel magic, but it can be breached and is subject to rust. The material component is a small sheet of iron.
The OD&D wall of iron had a maximum area of 5 square game-inches, and was always 3 inches thick. It wasn't permanent, having a duration of 12 turns. It had a range of 6" (0.5"/level in AD&D).
Wall of Stone: Creates a granite wall 20' square per level, and 1/4' thick per level. The wall doesn't have to be vertical, but it does have to be anchored to an existing stone formation, like a wall or a bridge. It's permanent unless destroyed with dispel magic or other regular means. The material component is a small block of granite.
The OD&D wall was always two feet thick, with a maximum height and length of 10". There was nothing about it needing to anchor to existing stone. It had a range of 6" (0.5"/level in AD&D).