To enable cheats go to the options menu and hold L+R, then input any combination you see below. If you do it correctly, you should here a sound then.
Drive red brick car: B(2), Y, X.
Drive as Smithers in Mr. Burn's limousine: B(2), Y(2).
Drive Nuclear Bus: B(2), Y, A.
Time trial mode: X, B, Y, A.
Slow-motion mode: A, X, B, Y.
No map display: Y, B(2), X.
Horizontal split screen: Y(4).
Hidden New Year's character: B(2), X, Y.
Hidden Halloween character: B(2), X, A.
Hidden Thanksgiving character: B(2), X(2).
Hidden Christmas character: B(2), X, B.
Nighttime mode: A(4).
Disable all active codes: Start(4).