Full Health
R2, R2, L1, R1, Left, Down, Right, Up, Left, Down, Right, Up

Full Armor
R2, R2, L1, L2, Left, Down, Right, Up, Left, Down, Right, Up

Tank
Circle X 6, R1, L2, L1, Triangle, Circle, Triangle

Increased Gore
Square, L1, Circle, Down, L1, R1, Triangle, Right, L1, X

Destroy All Cars
L2, R2, L1, R1, L2, R2, Triangle, Square, Circle, Triangle, L2, L1

Higher Wanted Level
R2, R2, L1, R2, Left, Right, Left, Right, Left

Lower Wanted Level
R2, R2, L1, R2, Up, Down, Up, Down, Up, Down

More Money
R2, R2, L1, L1, Left, Down, Right, Up, Left, Down, Right, Up

Speed Up Time
Circle, Circle, Circle, Square, Square, Square, Square, Square, L1, Triangle, Circle, Triangle

Change Costumes
Right, Down, Left, Up, L1, L2, Up, Left, Down, Right

Pedestrians Fighting
Right, R2, Circle, R1, L2, Down, L1, R1

Attacking Pedestrians
Down, Up, Left, Up, X, R1, R2, L1, L2

Pedestrians Riot
Down, Up, Left, Up, X, R1, R2, L2, L1

Crazy Pedestrians
R2, R1, Triangle, X, L2, L1, Up, Down

Improved Driving Skills
R1, L1, R2, L1, Left, R1, R1, Triangle. Press L3 or R3 to jump while driving

Dodo Car
R1, L1, R2, L1, Left, R1, R1, Triangle. L3 or R3 to jump

Urinate
Walk up to a wall and press Up, Down, Up, Down, L2, R1, R2, R2, Up, Down, Up, Down, Up. Your character will urinate on the wall. The cops will chase since it counts as vandalizing.

Infinite Run
To continue to run at a fast pace without fatigue, just tap X instead of holding it down. This helps when trying to give your character "exercise" so that he can run for longer periods of time as well.

Commercials

Websites

Official Site
DMA Design
Rockstar Games

GameWinners.com GTA3 site - TONS of cheats, tricks, and tidbits you never knew about.
Gouranga - Good news site.
GTA Scraper
Extracting Audio from PS2 DVDs - If you want to rip the radio stations or something. I did not use this method for the commercials on this page.