Unlock the Great Ones:
There are 4 different secret characters, moe, Bumble Bee man, Frink, and Ned Flanders. To get them you have to defeat them (ned is extremely hard! You must pin him twice to win the round. Cause god revives him.)

Unlock Itchy & Scratchy, Kang, And Smithers:
Beat the game in all 3 modes and you will unlock an option that enables you to play as Itchy & Scratchy for one level, Kang for another, and Smithers for yet another.

Beat Burns:
If you want to beat Mr burns run into the side and press X so he can't get you but he might throw fish so try to dodge them.

Unlock Bonus Match Up:
Enter the following at the PRESS START screen: Circle, Up, Up, Down, Down, Left, Right, Left, Right.

Unlock the Mayor:
Press R1, R1, R1 then triangle. Now the screen will say do you want to save press yes. Now the next time you go to chose a player the mayor will be there. this cheat will only work while your in a match.

The Homer Attack:
Pick Homer. Now when you have your invincibility ready. Get Homer to eat donuts (press 0). Right after he gets done activate your invincibility now pull out all your hits and just go crazy punching.When you do this the donuts increase Homer's attacks to big hits! Now that you can't die while you have invincibility Homer's best at close fighting so just tap!tap!tap!.

GameShark Codes

Enable Extra Characters
500004040000
800741e80001 
  
Enable Extra Circuits
80072bf00001
80072bf20001 
  
Unlock Bonus Menu
80072bd00001 
  
P1 Quick Pin
800e17ac0003  
  
P1 Cannot Be Pinned
800e18680000  
  
P1 Press L1 For Itchy
Use at Character Select screen. NOTE: You will ALWAYS fight Scratchy.
d00737d8fbff
8006e258000c 
  
P1 Press L2 For Scratchy
Use at Character Select screen.
d00737d8feff
8006e258000f  
  
P1 Press R1 for Kang
Use at Character Select screen.
d00737d8f7ff
8006e258000d  
  
P2 Quick Pin
800e18680003 
  
P2 Cannot Be Pinned
800e17ac0000  
  
P2 Press L1 For Itchy
Use at Character Select Screen. NOTE: You will ALWAYS fight Scratchy.
d00737dafbff
8006e278000c 
  
P2 Press L2 For Scratchy
Use at Character Select Screen.
d00737dafeff
8006e278000f
  
P2 Press R1 For Kang
Use at Character Select screen.
d00737daf7ff
8006e278000d 

Thanks to Revolution readers kyle stacey, SUNVIR, Peter Ham, mason counts and michael!