Infinite energy: 	
C-Up, C-Down, C-Left, C-Right, C-Up, C-Down, C-Left, C-Right.

Infinite ammunition:
C-Down, C-Down, C-Left, C-Left, C-Right, C-Right, C-Up.

Infinite time: 		
C-Up, C-Right, C-Left, C-Down, C-Up, C-Right, C-Left, C-Down. 

At the Main Menu, hold Z + L + R and enter the following:

Cyclone weapons power-up:
C-Left, C-Right, C-Down, C-Left, C-Right, C-Down, C-Up. 
You can also enable this by beating the Weapons challenge mode with a Bronze or better. 

Velocitar track: 
C-Left, C-Right, C-Up, C-Right, C-Left. 
You can also enable this by beating Race mode with a Bronze or better.

All ships: 
C-Down, C-Down, C-Down, C-Down, C-Right, C-Up, C-Left. 

Piranha II ship:

Beat Time challenge mode with a Bronze or better.

Super-combo challenge mode:

Beat all three challenge modes.

Thanks to Revolution readers Harrison Pantera, G-Licious, and Mike!