Level select:
At the main menu, press Up, Left, , , Left, Left, , Down, Up, .

Level skip:
During play, press , , Left, Down, Right, , Right, Up, X.

Invincibility:
During play, press , , Right, Left, , Up, Down, Down, Right, , .

Extra damage:
During play, press , , Right, Up, Right, , , Right.

Burn everything:
During play, press , , Left, Down, , .

Goat mode:
During play, press , Right, Left, Left, , , , Right, Up.

Thanks to Revolution readers Steven Landells and Adam Wilson!