There are sixteen magic-user spells of 7th level in AD&D, up from the nine that were in OD&D. The OD&D list has made the transition unchanged, and the remainder of the spells are all new.
Bigby's Grasping Hand: This is a more powerful version of Bigby's forceful hand, but rather than pushing targets away it grasps and holds them motionless. It can hold a creature of up to 1,000 pounds weight, and it can move creatures of up to 500 pounds away from the caster. The material component is a leather glove. I'm a little underwhelmed by the weight limit for such a high-level spell, but on the other hand it offers no saving throw, and it ignores the target's level and Hit Dice, so I guess it's a good way of taking out a high-level NPC.
Cacodemon: This spell is used to summon a specific, named Demon of Type IV, V or VI, which can then be bargained with to perform some sort of service. I'd be shocked if this spell wasn't one of the more oft-quoted passages during the 80s "devil's game" witch-hunts, as it has all sorts of language about making pacts with demons and blood sacrifices and whatnot, with little more than lip service given to the idea that this is something that would probably be restricted to evil characters.
There are three methods given for bargaining with a summoned demon. The first involves invoking the threat of the spiritwrack spell, which has a pretty good chance of turning said demon into your enemy. The second method involves the offering of human sacrifices, which is a little safer, but can still go wrong if the demon decides that the tribute is insufficient. The third involves using a trap the soul spell to imprison the demon within an inanimate object, which can be broken later on to release the demon to do the bidding of whoever just did the breaking. All throughout these descriptions it's reiterated that dealing with demons is dangerous, that they will turn a bargain against the caster at any opportunity, and that the proper protection is required to deal with them safely (protection circles, thaumaturgic triangles, and the like, which aren't really described in the Player's Handbook but are further developed in the Dungeon Masters Guide.)
As I mentioned above, the true name of the demon to be summoned is required for the spell. It's specifically stated that there are no demons weaker than Type IV whose names are known, and the spell is not strong enough to summon anything stronger than Type VI (like Orcus or Demogorgon). There's a chance with each casting that the demon named has already been imprisoned or destroyed in the past, or simply that the name has been pronounced incorrectly. In all of those cases, a new name will be required to attempt the spell again.
Material components are five black candles, a brazier of hot coals, sulphur, bat hair, lard, soot, mercuric-nitric acid crystals, mandrake root, alcohol, and a piece of parchment with the demon's name on it. It also requires a dish of blood from some mammal, preferably human, so there's blood sacrifice going on with this spell regardless of how the caster wants to use it.
Charm Plants: Plants in a 3"x1" area come under the control of the caster, and will obey his commands to the best of their abilities (including any special abilities a plant might have). Intelligent plants get a saving throw (with a -4 penalty). The material components are a pinch of humus, a drop of water and a twig or leaf.
The OD&D version of the spell had more specific limits on the number of plants affected based on size, rather effecting everything in a blanket area. It had a range of 12", which has been shortened to 3" in AD&D.
Delayed Blast Fireball: It's a fireball that deals 1d6+1 damage per caster level, that can also be delayed for 1 to 50 segments (a segment being 1/10th of a round). I've never, ever seen the delay effect used, but the extra damage dealt has always been appreciated.
Drawmij's Instant Summons: A non-living object no larger than a sword and no heavier than a shield can be instantly summoned into the caster's hand from anywhere. The item needs to be previously prepared, and a 5,000gp gem is also required for the preparation as well as the casting. The object can be summoned from other planes of existence (being able to traverse more planes the higher-level the caster is), but it can't be summoned if it's in the possession of someone else (although the spell will reveal the identity of the possessor). It's another spell that I'm not sure justifies its high level and exorbitant material requirements.
This is the first in-game appearance of Drawmij, a character from the Greyhawk campaign played by (who else) Jim Ward. Apparently the spell was created by Gary after a game where Ward's character had left a potentially life-saving magic item behind, and complained that wizards should have some means of summoning important objects to their hand. It's not clear whether the name Drawmij was coined by Gary for the spell and later adopted by Jim Ward, or if it happened the other way around.
Duo-Dimension: The caster becomes two-dimensional (losing the dimension of depth). Thus they can slip through cracks, and become invisible by turning sideways. While so invisible they can only be detected by a true seeing spell, and they are immune to all forms of attack. Otherwise, attacks on them deal triple the normal amount of damage. Recipients of this spell are partially within the Astral Plane, and can be drawn fully into it if noticed and attacked by a hostile Astral creature. The material components are a strip of parchment, and an ivory likeness of the caster worth 5,000-10,000 gp (which is consumed by the spell). Again, it's a spell that costs a hell of a lot to use.
Limited Wish: A spell that can pretty much do anything the caster asks for, within ill-defined limits. It can't create wealth or grant experience. Some examples that the spell gives are as follows: it can partially or temporarily restore hit points, reduce damage and hit probabilities of enemies, increase a spell's duration, change the disposition of a monster, or give minor clues to treasure or magic items. Greedy desires will often turn against the caster.
The OD&D spell is much the same, but doesn't bother to give any examples of what the spell can accomplish.
Mass Invisibility: Works like invisibility, but it affects a 3" x 3" area. Practically, this means that it can affect 300-400 man-sized creatures, 30-40 giants or 6-8 large dragons.
The OD&D version of the spell could affect 100-300 man-sized creatures, or up to 6 dragons. It had a range of 24", as opposed to 1"/level in AD&D.
Monster Summoning V: Summons 1 or 2 monsters of 5th level, that appear after 1-3 rounds. Looking at the Supplement I: Greyhawk tables (the only ones available at time of publication) shows a very nice spread of powerful monsters: trolls, ogre magi, wyverns, umber hulks, and even lammasu.
The OD&D version of the spell summoned but a single monster of 5th level.
Mordenkainen's Sword: Summons a "sword-like plane of force" that can be wielded mentally by the caster. It attacks as a fighter half the level of the caster, and can hit any creature (even those that are astral, ethereal or struck only by magical weapons). It deals 5-20 damage to a man-sized creature, 5-30 to anything larger, and will automatically hit on a 19 or 20 regardless of the target's AC. The material component is a miniature platinum replica worth 500 gp.
(I've already talked about Mordenkainen in an earlier post.)
Phase Door: The caster can pass through walls in a similar manner to the passwall spell, but a phase door is invisible to everyone else and can be used on multiple walls per casting. It can be dispelled by dispel magic cast by a higher-level caster. There's also an intriguing mention here of lower level casters being able to cast dispel magic in concert, and thus combine their levels for the purposes of the spell (though in this case they need to be double the level of the caster). This isn't something mentioned in the dispel magic description, so I'm wondering if it's just useful in this specific instance, or more generally? I rather like it.
The OD&D spell is similar, but it can be used 7 times per casting rather than a number based on the caster's level. The bit about casters combining their level for a dispel magic was also present in OD&D.
Power Word, Stun: Stuns any one creature for a number of rounds based on their hit points (4-16 rounds for creatures with 1-30 hp, 2-8 rounds for 31-60 hp, and 1-4 rounds for creatures with 61-90 hp). Creatures with over 90 hp are not affected. It should absolutely be noted that this spell offers no saving throw: it's an instant death sentence for any solitary creature that's under the hp limit (unless they happen to have magic resistance). It's also interesting that the spell goes off the creature's current hit points rather than their total. I tend to do the opposite in most cases.
The OD&D spell was similarly tied to the target's hit points, but it had a maximum cap of 70hp. This is understandable, as the hit points of monsters and PCs has increased on average since the spell was first created. It had a range of 12", whereas AD&D has changed that to 1/2" per level, shortening the range for the vast majority of casters.
Reverse Gravity: Affects a 3" x 3" square area, causing everything within that area to fall upwards for a single second. Apparently it can affect things even thousands of feet in the air, so it has no practical upper range. The objects "fall" 16 feet during that time.
The OD&D spell was the same, but it didn't have anything to say about the spell's vertical limit (or lack thereof). It had a range of 9", which has been changed to 1/2" per level for AD&D.
Simulacrum: A duplicate of the target is created from snow and ice. It is physically indistinguishable from the target, but is significantly weaker in level and hit points, and doesn't have the target's full knowledge. The simulacrum is mindless, and must be commanded by the caster. It can be given "vital force" with a reincarnation spell, and a limited wish empowers it with a portion of the target's knowledge and personality. The simulacrum can never gain levels. The material component is a powdered ruby, as well as a piece of the target placed within the snow or ice.
In OD&D, an ice storm spell was necessary if there was no snow present, and an animate spell was required as well (presumably this was changed to reincarnation). It's noted that the real person will be easily identifiable the two are encountered together. There's also a bit about the simulacrum gaining in strength if the original person is killed, which I like a lot. (On the whole, I would say that the OD&D spell is better explained than its AD&D counterpart.)
Statue: The target of the spell is transformed into a statue, and can change back and forth for as long as the spell lasts. The target retains all of its senses while a statue, and can be damaged, but is indistinguishable from a regular statue. Somewhat alarmingly, the use of the spell requires a system shock roll to survive, albeit one that's easier to survive than usual. The material component is lime, sand, and a drop of water stirred by an iron bar.
Vanish: The caster can cause an object to disappear, and reappear elsewhere at a location of their choosing. It has a weight limit of 500 gp per caster level. Heavier objects can be made to disappear, but when they "reappear" they are replaced by a like amount of stone.