Comic books based on video games are used primary to advertise and promote the video game in question. They usually come in the form of one-shots or a mini-series and are either prequels, set in the same universe or simply an adaption of the game storyline.
Notable Video Game Tie-in's
Sonic the Hedgehog
Published by Archie, Sonic the Hedgehog first appeared in 1992 as a 4 part mini-series and then in 1993 began its current ongoing series. Originally it was a light-hearted comic with single issue stories very much based on the Sonic video games but later on in the run it took on a more darker tone and had continuing storylines through multiple issues. After over 200 issues the Sonic the Hedgehog comic has created its own complicated history and is considered a separate reality to the Sonic video games.
Sonic the Comic
Unrelated to it's American counterpart, Sonic the Comic was released in the U.K. in 1993 by Fleetway. It was Sega's official comic and featured stories from many video games like Streets of Rage, Decap Attack, Golden Axe and Shinobi. The Sega stories began to appear less and less during the comics run, replaced by characters from the Sonic the Hedgehog strip like Knuckles and Tails. It lasted for 223 issues before the title folded in 2002.
Tomb Rider / Witchblade
Everything starts in New York, where Lara Croft makes her debut in comic books with Sara Pezzini. They embark on a crusade against a head of a mafia family.