At the main menu (the living room), go to the options screen, and then enter the codes... - A horn will confirm correct code entry. 

Invincibility: 
Hold down L + R, then press Y, A, Y, A.
Different Camera: 
Hold down L+R, then press B, B, B, A.
Fast Cars: 
Hold down L+R, then press X, X, X, X. 
Faster Cars: 
Hold down L+R, then press Y, Y, Y, Y. 
Grid View: 
Hold down L+R, then press B, A, B, Y. 
Pressing Horn Button Jumps: 
Hold down L+R, then press X, X, X, Y. 
View Credits: 
Hold down L+R, then press A, X, X, Y. 
Show Speedometer: 
Hold down L+R, then press Y, Y, B, X. 
Trippy View: 
Hold down L+R, then press Y, B, Y, B. 
One-Hit Wrecks: 
Hold down L+R, then press Y, Y, X, X. 
Unlock Red Brick Car: 
Hold down L+R, then press B, B, Y, X. 

Beat the Clock:
During timed missions the clock will not start until you get into your car. To get a head start simply run to the area you need to get to and then steal a car or visit a phone booth to get a car and continue the mission. 

Unlock Itchy and Scratchy Cartoon:
Collect all the cards in every level of the game to unlock an episode of Itchy & Scratchy 

Unlock Multiplayer Racing Game:
Collect all the cards in just one level to unlock the multi-player racing mini game. 

Holiday Look:
Change your system's internal clock to the dates for Thanksgiving, Halloween and Christmas to experience a different game look.