What are the different versions of Sonic the Hedgehog (1991) and what differs between them?

Sonic the Hedgehog

There were three official regional versions of Sonic the Hedgehog; REV00, REV01 and REVXB.

REV00 - Global

The original sonic was released for the Sega Genesis, in 1991. Sega identified the need for a company mascot, much like Nintendo have Mario. They were very successful - Sonic the Hedgehog was a hit success, and spawned many sequels and spinoffs. Sonic the Hedgehog was bundled with the Sega Genesis. The console was originally bundled with Altered Beast, and any player who had already purchased the console could request a copy of Sonic, for free.

REV01 - Japan and Korea

A revision of the game was released for the Japanese and Korean market, with quite a few changes. I went to sonicretro.org for a list.

• The "TM" symbol was removed from the Sega screen, as well as the title screen.
• Extra life granted every 50,000 points
• Level select order changed (previously in the wrong order)
• Level select cheat code changed from Up Down Left Right to Up Down Down Down Left Right
• Added some scrolling backgrounds, changed some others
• Changed the position of some level flags
• Fixed an interruption in the drowning music
• Tidied up some textures
• Minor changes to the Caterkiller, the labyrinth boss and the Final boss
• Killing the final boss awards a bonus 1,000 points
• Alternate Sega graphics
• Revision of code to allow certain functions to perform more efficiently
• Removed unused assets and code
• Further memory cleanup

REVXB - Japan

This revision was actually an official ROM hack. In this revision, spike damage was changed, to behave like it does in the newer titles.

Ports and Re-releases

The game is also packaged in many other games, sometimes as an unlockable.

• Sonic Compilation
• Sonic Jam
• Sonic Mega Collection
• Sonic Mega Collection Plus
• Sonic's Ultimate Genesis Collection
• Sonic Generations

It was also directly ported several times, including to the

• Android Play Store
• Apple iOS App Store
• Amazon App Store
• PlayStation Network
• Wii U
• Xbox Live Arcade
• Windows
• Steam

Ports may include changes relative to the console they are ported on. The biggest difference would be the controls. Some of the newer versions also included the addition of achievements.

Sonic the Hedgehog (8-bit)

Sonic was re-released, in 8bit, to accomodate the Sega Master System, and the Game Gear. Sonicretro.org lists no revisions, though the game did differ slightly on the game gear, to accommodate the platform.

Sega Master System Version

Levels were simpler, and had alternate themes, although the main objective of the game remained the same. It featured a different sound track, adapted from the original. If Sonic took damage rings were immediately lost, without giving the player a chance to recollect them. The Sega Master System version also contained no Sega splash screen, as this was provided by the console, on startup.

Game Gear Version

• Lower screen resolution.
• Increased colour pallete.
• Lighter controls.
• Sonic is smaller.
• Warning signs were placed in the starting area, as it was harder to see dangers ahead, with the smaller screen.
• Players would not take damage from falling.
• Redesign of the Labyrinth Zone, including alternate location of its Chaos Emerald.
• Modification of several bosses, including replacing some.
• Alternate Sega splash screen.

Sonic the Hedgehog Genesis

REV00 - Global

Sonic the Hedgehog was ported to the Game Boy Advance in celebration of its 15 year anniversary. It included the addition of new features, including the ability to save, and access to the level select without a code. It also included a new game mode, 'Anniversary Mode', where you could use the Spin Dash move from Sonic the Hedgehog 2. The view was slightly zoomed in, to accommodate the different screen resolution. It was poorly received, with claims of low frame rate, and poor game play preservation.

REV01 - Asia (uncommonly found elsewhere)

A new revision was released, although silently. This version was later ported to Wii and DS, and packed as an easter egg, in the games Sonic Adventure DX: Director's Cut and Sonic Mega Collection Plus.

There were a few changes, which I have sourced from tcrf.net.

• Overhall of the backgrounds and screen drawing. This meant significant graphical improvements, including scrolling clouds in Green Hill, and a ripple effect along water.
• Level select re-ordered to reflect initial intentions (original release featured the 'pre-release' order).
• New level select and Debug Mode, if played on a Japanese console.
• Included the point bonuses from Sonic REV01 - 50,000 awards a life, and the final boss awards an extra 10,000.
• Programming changes as were made from Sonic REV01, including the game over screen, boss behaviors and audio refinements.
• Programming cleanup, including efficiency improvements, and the removal of unused assets.
• Fixed a big where holding buttons at certain points would not cause Sonic to miss jumps.
• A secret was added to the first Labyrinth level, where the player could pick up an extra ring. The extra ring, by itself, was insignificant. However, this allowed the player to pick up a total of 50 rings in the level, and unlock that levels secret stage.

Sonic the Hedgehog (2013)

Sonic the Hedgehog was remastered, using the Retro Engine, for release on iOS and Google Play. It replaced the ports that were previously available. Additions included a widescreen graphic, the inclusion of the Spin Dash ability, a time attack mode, and the ability to play as Tails or Knuckles.

user106385 gave a quite complete answer.

I would add a point that I found very important for all games based on reflexes (so most of all):
Due to the 50Hz refresh rate of the PAL/Secam format in Europe, games played with European Megadrives and TVs run a bit slower than the 60Hz of NTSC format.
Particularly striking is how the music sounds different (not to speak about how the gameplay feels different).

Here is a video showing the differences:

And one explaining this difference more in details: