To access the Password screen, go to the Options menu, choose 'Game Status', highlight a character and press L+R.

Now enter the following passwords:

BLAST_FIRE      Stronger missiles
DRIVE_ONLY      Disables wheel attachment icons
GO_MONSTER      Big wheels
GO_RAMMING      Increases car's weight and ramming ability
GO_SLOW_MO      Slow motion 
HOME_ALONE      Solo play
JACK_IT_UP      Higher suspensions
LONG_MOVIE      See ending FMV 
MIXES_CARS      Can pick the same car in multi-player
MORE_SPEED      Faster cars
NO_GRAVITY      Reduced gravity
OLD_LEVELS      Play levels from the original Vigilante 8 
QUICK_PLAY      Instant action
RAPID_FIRE      Rapid fire
UNDER_FIRE      Enemies attack simultaneously

Special Moves:

Interceptor Missiles 
Halo Decoy:       Up, Up, Down, Machine Gun 
Afterburner:      Up, Up, Up, Machine Gun 
Missile Swarm:    Up, Up, Right, Machine Gun 

Bull's Eye Rockets 
Road Runner:      Up, Down, Down, Machine Gun 
Stampede:         Up, Down, Up, Machine Gun 
Bastion Rockets:  Up, Down, Right, Machine Gun 

Sky Hammer Mortar 
Turtle Turnover:  Down, Down, Down, Machine Gun 
Crater Maker:     Down, Down, Up, Machine Gun 
Tire Buster:      Down, Down, Right, Machine Gun 

Brusier Cannon 
Cow Puncher:      Down, Up, Down, Machine Gun 
Buckshot:         Down, Up, Up, Machine Gun 
Ricochet:         Down, Up, Right, Machine Gun 

Roadkill Mines 
Bear Hug:         Left, Right, Down, Machine Gun 
Cactus Patch:     Left, Right, Up, Machine Gun 
Hovering Mines:   Left, Right, Right, Machine Gun 

Flamethrower 
Brimstone Burner: Right, Left, Up, Machine Gun 
Oil Slick:        Left, Right, Up, Machine Gun 
Wall of Flame:    Right, Left, Down, Machine Gun 

Note on performing specials:
-You must have desired weapon in arsenal.
-Weapon doesn't have to be the selected weapon.

Hover Higher:
When hovering,double tap and hold the gas button to get a hover boost.

Thanks to Revolution readers Jorge Quiroz, fumo, Dean "ALLMIGHTY" Campbell, mark skellett, EvilGreg, NEO, and Janus 889!