I'm excluding Gen 1, as everything is pretty much built on top of it.
Sorry if I missed any.
- Two new types; Steel and Dark
- The Friendship Stat
- The Special Stat is split into Special Attack and Special Defense
- Shinies
- Pokérus
- Gender
- Breeding
- Hold Items
- No level skipping if a Pokémon gains enough EXP to grow two or more levels
- Weather
- Different Pokémon are available during different times of day
- Move Tutor (Crystal)
- Battle Tower (Crystal)
- Full Pokémon animations (Crystal)
- Abilities
- Natures
- Revamped Boxes
- Slightly different movesets in FRLG/Emerald to Ruby and Sapphire
- Moves have Contest Stats
- Double Battles
- Improved IV system
- Improved EV system
- Different main villains, depending on which game you have (Ruby and Sapphire)
- Stat reducing Berries (Emerald)
- The Battle Frontier, which is like a post-game version of Stadium (Emerald)
- Moves are now designated physical or special based on the move itself, rather than its type
- No more caps lock for Trainer names by default
- Many Pokémon have gender differences
- Hatchlings are level 1, instead of level 5
- Slightly different movesets in Platinum/HGSS to Diamond and Pearl
- Pokémon have Characteristics
- Double battles against wild Pokémon
- Trainers are Animated
- Record and share battles through wifi (Platinum and HGSS)
- Each Pokémon has Pokéthlon Stats (HGSS)
- Some Pokémon get access to new Breeding Moves (HGSS)
- Dream World Abilities
- Dream World exclusive Moves
- Triple Battles and Rotation Battles
- Can capture wild Pokémon in Double Battles
- Shaking Grass/Rippling Water/Rustling Dirt/Shadows
- Different Pokémon can appear, depending on the Season
- You can see each Pokémon's full Back Sprite
- TMs last forever
- No Poison seizures
- Some (may just be one) Pokémon have/has different Mini Sprites to Gens 3 and 4
- More likely to get mother's Ability while Breeding
- Pokémon and Move names aren't all in caps
- Hard and Easy Modes (B2W2)
- Battle Frontier replaced by PWT (B2W2)
- Fairy Type
- Mega Evolutions
- Some Pokémon have a slight BST increase
- Easier to EV Train Pokémon
- Hoard Battles
- Sky Battles
- Inverse Battles
- Trainer customization
- Gain EXP after Capturing a Pokémon
- Pokémon can evolve after a battle, even if they're KO'd
- Revamped Mini Sprites
- Revamped Pokémon Cries
- Can get Egg Moves from both parents
Sorry if I missed any.