So I wanted to expand on an idea that I used to have. I really do think that there should be certain items (read as: Assist Trophies and a Poke Ball) that allow for a new "riding" mechanic.
Essentially, these "mount" characters would allow for better traction, faster movement, and a new attack. To dismount, press the B button. Pressing A will perform the mount's attack.
Some possible mounts:
Donkey Kong Country: Rambi - A charge attack
Pokemon X and Y: Gogoat - Horn Leech
Fire Emblem: Caeda (No, not like that. You'd ride on the back of her pegasus as she steers :D) - A lance charge by air.
Super Mario Galaxy 2: Fluzzard (Yoshi would be the obvious Mario Mount, but he's playable. - Talon attacks
Kirby's Return to Dreamland: Landia - Fire Breath
Legend of Zelda: Epona - A fierce horsey kick.
Just an idea. Feel free to bash it. Or add other ideas. Whichever one's fine.