Sonic 3 (and Knuckles)

Sonic 3 and Knuckles

Method 1: Original Hardware

Consoles

Sega Mega Drive: The original console that Sonic 3 and Knuckles was released on. It should be noted that this game was seperated into 2 games (Sonic 3 and Sonic and Knuckles respectfully) due to the hardware limitations that the Mega Drive had.
PC CD-ROM: Finally, a CD-ROM for Sonic 3 and Knuckles was released as the "Sonic and Knuckles Collection". However, there is no way of obtaining this version of the game anymore.
PlaySEGA: A PC version of the game playable in browsers with flash enabled was available from 2008 to 2011. Unfortunately, it does not seem as though this version of the game is backed up on the Internet Archive as of this current moment.

Semi-Available Methods

The following official releases are still technically available if you own the game on said platform, but are no longer sold due to the game being added to Sonic Origins, which is a compilation game that contains every single classic mainline game.

Steam
Xbox (in general): Something to note about the Xbox in particular is the the game has been released on every version of the Xbox.

Game Compilations

Many of the classic games such as Sonic 3 have been released in different game compilations. These are essentially re-releases of these games, but they are bundled together with other games to create one game with multiple games.

Sonic Origins (and Sonic Origins Plus): This is the most accessible game compilation to play this game on. Sonic Origins is available on Steam, the Epic Games store, Xbox One and Series X, Playstation 4 and 5, and the Nintendo Switch.
Sonic Jam: This game compilation was released on the Sega Saturn.
Sonic and Garfield Pack: This game pack for Sonic 3 was released for the PC alongside Garfield: Caught in the Act and Baku Baku.
Sonic Mega Collection: This game compilation was released for the Gamecube and is backwards compatible with the Wii.
Sonic Mega Collection Plus: This game compilations was released for the PC, Playstation 2 (and is backwards compatible with the Playstation 3) and the original Xbox (and again, is compatible with the Xbox 360)
Sonic Classic Collection: This game compilation was released for the Nintendo DS and is backwards compatible with the Nintendo 3ds.

Method 2: Dolphin Emulator

This serves as another method to play the game. All you need is just a Gamecube copy of the Sonic Mega Collectione and a little determination and you'll be able to play this game on your computer. If you want to use Dolphin Emulator to play this game, go here to learn how to set up Dolphin Emulator.