Sonic 3 & Knuckles

Stage Select & Sound Test:

Start the game and grab to the first vine (I recommend Tails for this job, you'll save time as you won't see the Super Sonic intro, and you can fly to grab to a vine). Once grabbed, press Left, Left, Left, Right, Right, Right, Up, Up, Up. If you've done this correctly, you'll hear a ring. Now you can pause the game and press A to reset. To enter the Stage Select, press Down twice in the 1 PLAYER/COMPETITION menu and select SOUND TEST.
Notice the Lava Reef act 3 and act 4 present in the menu. Lava Reef act 3 is actually Lava Reef act 2, boss area. Act 4 is Hidden Palace. Sky Sanctuary act 1 is the level you play with Sonic, act 2 is the final level for Knuckles. Death Egg shouldn't be playable with Knuckles, but you can! Go for a "new" level! (Some things may block you, however, like the boss of the act 1.) Doomsday act 1 is the final level with Hyper Sonic, and Doomsday act 2 is actually the giant Robotnik robot boss from Death Egg Act 2. Special Stage act 1 will get you into the next Special Stage you need (you can get an emerald, reset, enter the Stage Select again, get the next, reset, and so). Act 2 will warp you to a new, extra 3D bonus stage. Get its Super Emerald and watch for a weird thing to happen...
Having highlighted any stage, you can change the value of the number between Angel Island and Hidrocity with C, to select your player. 00 is for Sonic & Tails, 01 for Sonic alone, 02 for Tails alone and 03 for Knuckles.
In the Sound Test, you'll find some unused music from Sonic 3 (like 26h). There are many unused sounds, too (some of them from Sonic 2). Some of the last sound codes are not sounds but effects, which will modify the speed of the music playing, fade it, etc.

Slow Motion:

With the Stage Select cheat enabled and the game paused, A will return reset the game, C will advance a single frame, and B will put the game in slow motion (you can move and jump with C). You'll hear the music in slow motion mode, but it will be glitchy. This is the correct behavior in the original console. However, in GENS, you'll hear the normal music at normal speed instead but this seems to be a bug in the emulator.

Debug Mode:

Make the Stage Select cheat and enter Mushroom Hill. Grab to the first pull-up machine, then press Left, Left, Left, Right, Right, Right, Up, Up, Up. If you've done this correctly, you'll hear a ring. Now you can pause the game and press A to reset. Now, you can start a normal game with A without releasing it until the character appears, or go to the Stage Select and enter any stage with A[Start], without releasing A until the character appears.
During the game, C will make the character to jump, A will invert the gravity (and it does work in zones other than Death Egg, so you have a new world to explore!), and B will change between play mode and object placement mode. In object placement mode, D-Pad will move the cursor (you can fly), A will change the object and C will print it in the stage. You can add almost anything to the stage, including weird objects in some stages, but it will disappear if you go one screen and a half away horizontally. You can use the Debug Mode in a 2 Player VS stage, but the behavior is sometimes undefined. In object placement mode, the Score text will display the offsets for the cursor, instead of your score; and the number of seconds in Time will be the number of active sprites. You can turn into an object while dying, to avoid it. Even you can press B in a cylinder, elevator, or many other special things, but the screen will have glitches until you press B again. You can place special Super Sonic monitors, which will be worth 50 rings and turn you into Hyper Sonic, Super Tails or Hyper Knuckles.
With the Debug Mode, you can go to the Stage Select and enter stages not designed for the character you've chosen. For example, you could fight Super MetalSonic with Tails. But the game may mess up or even crash at the endings with unexpected characters, the palette could be wrong in the ending, and Tails or Knuckles will look weird in Super Sonic's Doomsday Zone.
There is a bug, which can be used to turn the player into another object (but with glitches). Find one of those big rings to go to a 3D bonus stage, and enter it. Just after you disappeared, press B. Play through the 3D bonus, and when you finish it, you'll be looking like the object you were when you entered the Special Stage. Try this with a monitor.

Character Sprites Show:

Activate the Debug Mode in any level, and press C to jump and very quickly B. Instead of going to object placement mode, you will see all the sprites of your character, one in each frame. Press B to return to play mode. Tip: You might want to use Start, then C, to advance frame by frame and see every sprite. In Genecyst, you can capture the sprites using this trick and disabling all background layers but one (so you'll get every sprite in a single color background). Note: Tails has new sprites not present in Sonic 3!