Put a game other than Sonic 2 or 3 in the top of the Sonic & Knuckles cartridge. Then, when it shows the picture of the trio and the message at the top, press A, B, and C simultaneously to play Bonus Games.
Contributed by: Igtenos
Level Select (when not Locked-On to anything else)
In Mushroom Hill Zone, while hanging off one of the pulling machines, press left three times, right three times, and up three times. You should hear the ring sound. Pause and press A to be taken to the title screen. Highlight either Sonic or knuckles as your character, and press start while holding A. The menu shows all levels in the game, but some are specific to a certain character, so you can't play those if you picked an incompatible character. Any time you want to exit and select a different level, just repeat the code from right after the pulling machine part.
Contributed by: KANGASKHAN
Walk through walls
On levels that allow you to travel upwards or downwards greatly as you progress as Sonic, go to an area where Knuckles' path starts. Hold down and wait for the screen to drop, then jump (do not spindash). If done correctly at a area that will cause this, the screen will shift and scroll in a loop back to you. During this time, you are free to walk through walls. This can also be done in select areas of levels where there is no path for Knuckles.