Secret Options Menu
While holding L at the character select menu, input the following:
C-Up, C-Right, C-Left, C-Down, B, A

Then go to the option menu and you will see a new menu for Secret Options. Now you can choose itty bitty/massive bodies, high/low voice, background select, and a few other options!

Play as Booger Man
Holding down the left shoulder button (L) at the character selection screen, move joypad Up, Right, Down, Left, Right, Left.

Play as Dr. Kiln
If you beat the game on psycho, you receive the following code:
Holding down the left shoulder button (L) at the character selection screen, hit: B, C-Left, C-Up, C-Right, C-Down, A.

Play as Sumo Santa
Holding down the left shoulder button (L) at the character selection screen, hit: A, C-Down, C-Right, C-Up, C-Left, B.

Play as Earthworm Jim
Holding down the left shoulder button (L) at the character selection screen (highlight ?), hit: B, C-Left, C-Up, C-Right, C-Down, C-Up

Play as High Five
Holding down the left shoulder button (L) at the character selection screen (highlight ?), hit: Up C, Down C, Left C, Right C, B, A. Release L and press R to make High Five appear in that box.

Random Character Selection
Hold down the 'R' and 'L' buttons at the character selection screen and a random fighter will be chosen.

Claytalities
Blob's Pincer: stand at sweep distance hold L and press down, down, forward, and R
Bonker's Exploding Drum: stand at sweep distance and press forward, down, and forward
Dr. Kiln's Death X-Ray: stand at sweep distance and press back, down, down, and forward
Taffy's Fireworks: stand at sweep distance and press back, forward, back and, forward
Ickybod Clay's Scary: stand at sweep distance and press down, down, forward, back and, R