China Town Jam track:

Complete Grand Prix mode in first place on each track under the "Expert"
difficulty level. 

Neo Speed Way track:

Complete Grand Prix mode in first place on each track under the
"Intermediate" difficulty level. 

Nintendo 64 controller vehicle:

Begin game play in time attack mode. Keep racing until obtaining a time
that ends in .064 seconds. Press R when selecting this vehicle to change
colors from red, green, blue, black, or yellow. 

Dominator vehicle:

Complete the game in first place with the Black Lightning under the
"Expert" difficulty level. 

Prowler vehicle:

Complete the game in first place with the Hornet under the "Expert"
difficulty level. 

Reaper vehicle:

Complete the game in first place with the Shredder under the "Expert"
difficulty level. 

Vengeance vehicle:

Complete the game in first place with the Avenger under the "Expert"
difficulty level. 

All tracks and vehicles:

Hold L + R + Z on controller two before the title screen appears. Keep
those buttons held, then quickly press and release Up + C-Down on
controller two when "Push Start" flashes on the title screen. Then,
press Start on controller one before the title screen disappears. Note:
The timing of this code is particularly sensitive; all buttons must be
pressed and released at exactly the same time as indicated. 

Alternate vehicle color:

Highlight a vehicle on the selection screen, then press R. 

Quick start:

Hold A + B before the race begins. Release B immediately after the
commentator says "Ready". 

Turbo:

Begin game play and hold A to speed up. Hold Z and press Analog-stick
Left or Analog-stick Right, release A and Z, then quickly press A + Z.
A sound will confirm correct code entry. 

Faster Grand Prix credits:

Press Start when the credits appear after a Grand Prix.