All Characters Are 2 Dimensional:
To turn all of the characters into 2D, similar to cardboard cutouts go to the options screen and Hold in the L and R buttons and enter in the following code:
X, X, X, X

Clear All Codes:
To clear all the codes you have entered, click L and R at the options screen and enter:
Start, Start, Start, Start

Debug Mode:
To enter a sort of debug mode, where all objects are surrounded by lines go to the options screen and Hold in the L and R buttons and enter in the following code:
B, B, A, A

Extra Camera Angles:
To get additional camera angles, such as Top View and Look Mode go to the options screen and Hold in the L and R buttons and enter in the following code:
B, B, B, B

Homer's Secret Ride:
Complete all 10 missions on mission mode. Then select Homer to use his new car.
Source: ign.com

Nighttime Mode:
To drive through the streets of Springfield at night go to the options screen and Hold in the L and R buttons and enter in the following code:
A, A, A, A

Skip Missions:
Missions 1 through 9 can be skipped if you fail them 5 times. The last mission, however, cannot be skipped. Also note that skipping the missions does not prevent you from getting your reward, The Homer.

Slo-Mo Mode:
To turn all of the characters into 2D, similar to cardboard cutouts go to the options screen and Hold in the L and R buttons and enter in the following code:
A, X, B, Y

Stop Watch Mode:
To enter Stop Watch Mode go to the options screen and Hold in the L and R buttons and enter in the following code:
A, X, B, Y

Turn off the map:
Go to the options screen and hold in the L & R buttons while entering Y, B, B, X. You will hear the confirmation sound, and this will turn off the small map on the lower left corner of the screen.

Unlock Frankenbart:
To unlock a Halloween Bart Simpson, set your GameCube's date to 10/31. Bart will appear as Frankenstein on the character select screen (under the ? category).

Unlock Marge the Pilgrim:
To see Marge all dressed up like a Pilgrim, set your GameCube's date to Thanksgiving day (November 22). Marge will be selectable at the character select screen.
Source: ign.com

Unlock New Year's Krusty the Clown:
To unlock a special holiday suit for Krusty, set your GameCube's clock to January 1. Krusty, in his spiffy duds, will be selectable from the Character Selection screen.
Source: ign.com

Unlock Santa Apu:
To see Apu dressed as Santa Claus, set your GameCube's date to December 25. The jolly Kwik-E Mart owner will then be available on the character select screen.
Source: ign.com

Use "Box" Car:
To drive as a small red box with no driver go to the options screen and Hold in the L and R buttons and enter in the following code:
B, B, Y, X

Use Burns' Car:
To drive as Smithers in Burns' Car go to the options screen and Hold in the L and R buttons and enter in the following code:
B, B, Y, Y

Use Christmas Apu:
To drive as Christmas Apu (no matter what the date) go to the options screen and Hold in the L and R buttons and enter in the following code:
B, B, X, B

Use Halloween Bart:
To drive as Halloween Bart (no matter what the date) go to the options screen and Hold in the L and R buttons and enter in the following code:
B, B, X, A

Use New Years Krusty:
To drive as New Years Krusty (no matter what the date) go to the options screen and Hold in the L and R buttons and enter in the following code:
B, B, X, Y

Use Nuclear Bus:
To drive as the Nuclear Bus go to the options screen and Hold in the L and R buttons and enter in the following code:
B, B, Y, A

Use Thanksgiving Marge:
To drive as Thanksgiving Marge (no matter what the date) go to the options screen and Hold in the L and R buttons and enter in the following code:
B, B, X, X