While playing a game, press L1 + L2 + R1 + R2 + Select + Start.
NTSC Cheat mode
Enter "2GSH" as a player name to unlock all characters, courses, balls, clubs, goodies, and the "Top-Pro" level. With the "Top-Pro" status, it also unlocks difficulties.
PAL Cheat mode
Enter 2GE as the player name. This gives you all characters, clubs, courses, goodies etc.
Unlock secret characters
Every time you beat a character in vs. mode, you unlock it. You can even get Sweet Tooth from Twisted Metal, Gex, and Sir Dan from MediEvil. When you have unlocked all the regular secret characters you will also get a chance to unlock the 13 characters from the original Hot Shot's Golf.