Well, this thread is for new characters, but I'm just going to run through the MBST file I have for Smash 4...
Bayonetta:Bacon Binger
Captain Falcon: The Crappy Captain
Cloud: FART CLOUD
King Dedede: Wii Fit Trainer Killer
Diddy Kong: The Masked Kong!
Donkey Kong: Disgusting Ape Thing
Dr. Mario: Quack 64
Duck Hunt: Duck, Duck, DIE
Falco: Hey Einstein! I'm on your side!
Fox: Leader of Star Bucks
Game & Watch: The Mister!
Ganondorf: The Main Character
Greninja: Master of Being Dissected
Ike: The Famous Candy Bar
Corrin: Syrup of Maize
Kirby: Dumb as a Brick
Bowser: Wowser, you da best!
Bowser Jr.: Pac-Pwner
Link: The Ultimate Joke
Little Mac: The Tiny Big Mac
Charizard: Doofus Dragon
Lucario: Lucardiac Arrest
Lucas: Brownie Boy
Lucina: Look How Pretty I Am
Luigi: The Gayest Brother
Mario: Badass Fatass
Marth: The Tiara-Queen
Meta Knight: The Meaty Murderer
Mewtwo: Aborted Cat Fetus
Mii Fighter: The Barlwer of Wario's Bellies
Mii Gunner: The Gunner of Wario's Noses
Mii Swordfighter: The Swordfighter of Wario's Smells
Villager: Mayor of Starcraft
Ness: The Funny Fudge Freak
PAC-MAN: THE Sorriest Excuse EVER
Palutena: Goddess of Pie
Peach: Princess... PITCH!
Pikachu: Oh my gawd!
Olimar: Veteran Wii Fit Killer
Pit: Needs Deodrant
Dark Pit: Too Late for Deodrant
Jigglypuff: Pop Goes The Puff
Robin: The Burger King
R.O.B. :RRRRR! Freak
Mega Man: The Blue Soda
Rosalina: Laser Surgeon
Roy: ROOOYYY!!!
Ryu: Talk is Cheap
Samus: Research Robot Extraordinaire
Sheik: Sheik Shookoo Shaka
Shulk: Are you feeling it?
Sonic: The Fast Freak
Zero Suit Samus: Robot Stunt Double
Toon Link: Farore-Forcing Failure
Wario: Cute Man with a Fart of Gold
Wii Fit Trainer: Pikmin Fodder
Yoshi: The Green Snotbag
Zelda: Hyrule's Famous Yelling Woman
Metal Mario: You Can't Kill the Metal
Ellis: Have I Told You About Keith And
Mr Krabs: The Crustaceous Cheapskate
Another Mario variant?: Sugar Makes You Fat!
Peter Griffin: The Killable Family Person
Waluigi: Walu-Useless
Wendy: The Brat Who Wants America
Alph: Wii Fit Killer in Training
LeftyGreenMario: KlutzyGreenMario
Mario (swim trunks): Flabulous Italian