While most of the changes between 1st edition and 2nd edition AD&D were minor enough that both could easily be seen as two versions of the same game, the designers of 3rd edition D&D started from scratch and overhauled everything. What follows is a very incomplete list, as there are far too many changes to list here.

Characters

Combat

  • Rounds of combat last six seconds.
  • Initiative is rolled only at the beginning of a combat; the initial order of action is generally kept throughout the rest of the combat. After the first round, there is no more "first" or "last", only "next" in a repeated cycle of actions. There are ways to change where a character is in that order, however.
  • There are only three saving throws for characters: Reflex (getting out of the way), Fortitude (withstanding massive physical damage), and Will (fighting off mental attacks).
  • The rogue's "backstab" is now a "sneak attack," and can come from any direction. Instead of a damage multiplier, it does an extra 1d6 damage at 1st level, 2d6 at 3rd, 3d6 at 5th, etc.
  • Critical hits in the form of damage multipliers are now part of the standard rules. A roll of natural 20 is not always required for a hit to be critical.
  • Except for damage, almost everything is based on the roll of a d20. High is always good, low is always bad. In most cases, a natural 20 will always succeed and a natural 1 will always fail.
  • THAC0 is gone; AC now starts at 10 and goes up. If the rolled number plus modifiers is equal or higher than the target's AC, it is a hit.
  • Polearms have "reach" and are generally only useful if an opponent is ten feet away.
  • Which direction a character is facing does not matter in combat. Instead of bonuses to hit for attacking from the side or rear, whenever two characters are on exactly opposite sides of the opponent they are fighting, they get a bonus to hit. If the opponents are thieves, they can "sneak attack" every round that they remain on exactly opposite sides of the opponent.
  • Unarmed combat has been overhauled and streamlined.
  • Characters are unconscious and dying if their hit points fall below 0, and die when their hit points reach -10.
  • Each character in combat "threatens" an area for 5 feet in all directions. If an opponent attempts certain actions within this area, the attacker gets an attack of opportunity on that character.
  • Use of miniatures of some sort (even just dice on a grid) is strongly recommended, due to the many instances where relative position of combatants and distance between combatants is vital to running a combat.

Spells

  • All spells are now in a single alphabetical list, with a line in each describing which classes can access it and what spell level it is for each class.
  • All spells have been extensively overhauled, with many added, dropped, renamed, altered beyond recognition, etc.
  • Magic resistance is now called "spell resistance."
  • The cleric spell list has been rearranged to be on a 9-level scale instead of a 7-level scale.
  • All spell writeups now include a comment about how spell resistance applies to the effects of the spell.
  • Spells generally have casting times of 1 action, 1 round, 1 minute, 1 hour, etc. Mages who cast a 1 action spell can also move up to their full movement for the round. Mages who cast a 1 round spell can move up to 5 feet that round.

Monsters

  • Monsters do not all get d8 for hit dice; some may get d4, others may get d12. Bonuses to the final hit point total can now far exceed +3. All monster listings include the average number of hit points, so that "standard" examples of that creature can be easily created without rolling dice.
  • There is now a save against undead energy drain to see whether it is temporary or permanent. Energy drain gives a character "negative levels," which apply a cumulative -1 to all rolls and will kill a character if they are equal or greater than the character's Character Level.
  • Monster xp now varies depending on how much of a challenge the encounter is to the PCs.
  • Special abilities are listed as Extraordinary, Spell-like, or Supernatural, to better judge how they interact with other abilities (such as spell resistance) and whether or not they can be disrupted in combat.
  • Monsters now have STR, DEX, CON, INT, WIS, CHA, as well as saving throw bonuses, just like PCs.
  • Monsters can gain levels in "character" classes, and their monster hit dice count as levels of "Monster."
  • Dragons have been made significantly more dangerous and deadly than before.

Miscellaneous

  • All PCs, NPCs, deities, and locations mentioned in the PH and DMG are taken from the world of Greyhawk.
  • Far, far too many details to list here.

Changes courtesy of the rec.games.frp.dnd faq.