On the Spike Hoppin' title screen, hold down buttons 1, 3 and 4 to access the game.
Infinite lives and level skip
Start a game, but don't score any points. Repeatedly jump off the top platform so Spike won't land on any others. Do this until you have one life left, then hold down button 4 and jump. This gives you infinite lives, and to skip to the next level, press button 1 when a level begins.
See Voyager fly-by
When the copyright screen appears, hold down buttons 1, 2 and 4 until the Star Trek Voyager ship appears.