Level Select
At the title screen press up, down, left, right. You should hear a ring chime. Hold the A button and press Start.
Debug Mode/Invincibility
At the title screen press up, C, down, C, left, C, right, C. You should hear a chime. Hold A and press Start. If you have previously done the Level Select cheat, you will enter the level select menu. Simply hold A and press start on the level you wish to play. In debug mode, press A to toggle between be a sprite and Sonic. While a sprite, press B to enumerate amongst the sprites. Press C to place the sprite. Note that Sonic is now invincible against most things. He will still get hurt, but not die. This has an unusual side affect in version 1 of the US release. If he lands on a row of spikes, he will jump to the next row. As a result of the spike glitch, he will jump back to the first one creating an endless cycle.