At the Options screen, hold L + R and enter the following:

Invincibility:
Y, A, Y, A

Faster cars:
X, X, X, X

Much faster cars:
Y, Y, Y, Y

Instant explosion:
Y, Y, X, X

Super jumps:
X, X, X, Y. Use the horn to jump.

Alternate view:
B, B, B, A

Show speedometer:
Y, Y, B, X.

Grid view:
B, A, B, Y

Freakout view:
Y, B, Y, B

Thanks to Revolution readers Mark, Awol, bubba88 and Joel!