Bust-A-Move 2 Arcade Edition
Bonus Characters
Start a new Puzzle game, and at the screen where you choose your path, press Left, Left, Up, Down, L, R, L, R, L + R. If you do it it right, a Character Select screen will appear.
Credit Goes To: Erik Pfannkuche via N64cc
 Bonus Characters
 Level Skip
 Another World
 Extra Puzzles
Level Skip
While playing press: Z, R, L, and A simultaneously to skip to the next stage.
Credit Goes To: CODE MAN via IGN 64

Another World
At the main menu screen that reads, "Game Start", Time Attack", and "Options", enter L button, up on D-pad, R button, and down on D-pad. This will give you access to "another world" full of new puzzles. After entering this code, a tiny character will appear in the lower right portion of the screen. Select "game start" and when you select "Puzzle Game", it will say "Another World" underneath it.

Extra Puzzles
For more puzzles, press A, Up, B, Down at the Title Screen.
Credit Goes To: IGN 64