Mario: Pipe.
Luigi: Pipe.
Peach: Appears in some hearts with the parasol.
Bowser: Wall of flames.
Donkey Kong: DK Barrel
Diddy Kong: DK Barrel
Yoshi: Egg
Wario: Bike
Link: Tornado, LoZ reference. The ONLY one that changed from SSB, where he descended from a ray of light like in OoT.
Zelda: Magic. Sheik: Same.
Ganondorf: Purple fire.
Toon Link: Explosion.
Samus: Save port. Zero Suit: Power Suit falls off.
Pit: Ray of light
R.O.B.: Assembled
Ice Climbers: Condor
Kirby: Warp Star
Meta Knight: Appears in a whirl
King Dedede: Delivered by Waddle Dees
Olimar: Hops out of rocket, plucks three Pikmin
Fox: Arwing
Falco: Arwing
Wolf: Wolfen
Captain Falcon: Blue Falcon
Pikachu: Pokéball
RED: Is there, throws Pokéball
Jigglypuff: Pokéball
Lucario: He just happens. No parents.
Marth: Warp magic
Ike: Warp magic
Ness: PSI Teleport α crash.
Lucas: Mr. Saturn's tea table
Mr. Game & Watch: LCD frames
Snake: Stealth camouflage fails
Sonic: Shows up
Link's was the only one with a major change. Lots of characters like Mario and Pikachu pose differently, Captain Falcon now does not pose, instead taking time to exit the car, you can now see the portal when Ness appears, etc.