Most unique of the potential fighters in my opinion.
Toon Zelda
Toon Zelda's unique ability is that she starts out in a super heavy, powerful suit of armor with strong, heavy attacks. The more damage she takes, the more of her armor falls off, making her lighter. Eventually the armor will break and you will be playing as Spirit Zelda. Unlike her Phantom form, she has no special attacks other than her ability to channel her energy (similar to Wii Fit Trainer) so that she can regain her armor.
Though she is a spirit, you can still attack her and she can use non special attacks. She also has the option (When wearing Phantom Armor) to shed her armor with an explosion as a down special.
The difference here between Zelda & Sheik is that Toon Zelda's different forms are not different fighters, although they do have different attacks. It's merely switching between whether you want to be slow, but powerful or quick, but weak. They are not separate characters with unique data, Final Smashes, victory poses, etc.
Paper Mario
Paper Mario's unique ability is that he is actually a stack of FIVE Paper Marios. He can separate and multiply as well. After losing his copies, he becomes the lightest character in the game.
Balloon Fighter
Balloon Figher is kind of a reverse Little Mac. He's quite useless on the ground, but a supreme aerial fighter. He uses his down special to pump more balloons, kind of like Olimar becomes more useful with more Pikmin.
Other unique abilities include sparks, flippers, and an up aerial that releases a balloon into the air that pushes the opponent up (like Mega Man's up aerial) which eventually gets bigger and pops.
Captain Toad/Toadette
Captain Toad's unique ability is that once he takes excessive damage, he shrinks to Small Captain Toad. He can also summon help from the members of the Toad Brigade. He can't weild them like Pikmin, but it makes him a "follow the leader" type character.
Takamaru
A sword that can swipe through anything and the ability to turn invisible.
Bomberman
Has a move set that revolves around explosives.
Simon Belmont
Simon's whip makes him the only character with a weapon that has physics as well as a weapon with eight directional attacks instead of four.