To play as everyone's favorite wallcrawler (but not a mutant), Spider-Man, defeat the webslinger in Arcade Mode. Continue untiul you beat arcade mode. Then, when it's time for character selection, highlight Cyclops. Press L1 to select Spider-Man.

To unlock Professor X as a playable character, beat the entire Arcade mode with Juggernaut. After you've won, you'll be able to select "Wheels" by highlighting Magneto and pressing L1.

To unlock the mutant vixen Psylocke, defeat the Arcade mode with Wolverine.

You have some work to do to unlock Juggernaut. You'll have to beat the game with everyone (including Psyclocke) to open up the heavy beast.

This is the big one! The master code unlocks everything in the game: all characters, all FMVs and alternate costumes. To activate it, go to the title screen, then press SELECT, DOWN, R2, L1, R1, L2.