Splatterhouse 1 was released in 1988.
Splatterhouse 2 was released in 1992.
Splatterhouse 3 was released in 1993.
Splatterhouse: Wanpaku Graffiti was released in a Japan-only version in 1989. This game features the characters as mostly SD chibis and is not graphic like the other games are.
Splatterhouse Remake (not official title), was released on November 23rd of 2010 for Western markets and is a 3D third person remake of the first game.
In the games, the player controls Rick Taylor, a man who has, through his fusion with an Evil Mask, become extremely strong and who resembles to a great degree Jason Voorhees, of the Friday the 13th movies.
The games take place in a variety of locations, but all have a common setting, in and around a frightening mansion filled with disgusting demons and monsters.
The point of the games, with the exception of part 3, is to save Rick's girlfriend, Jennifer, who has been targeted for one reason or another by the various demons and evil forces that inhabit the game's localities.
In part 3 the player must use the map to find and save both Jennifer and their child from the demons, so it differs from the other games, which are mostly 2d side scrolling. Part 3 differs also because time limits are in place for the family saving mission portions of the game. Part 3 also differs in that Rick can 'power up' himself for a brief time to use vastly increased physical power to do drastic damage, as well as using some special moves. Finally, part 3 differs because enemies can be grabbed and slammed, headbutted, etc.
Rick can punch, kick, jump, equip various melee weapons, and perform a sliding kick. In most instances, his strength is evidenced by the brutal mutilation of the enemies due to the hitting power of his attacks. For example, zombie like enemies burst in half when struck. In part 2 and 3, it is revealed that the mask which granted him this power has an infernal, evil personality.
Weapons include: 2x4, Lead Pipe, Explosive Potion, Cleaver, Shotgun, Rock, and others.
It is suggested by the storyline of the first two games that the monsters have come about due to an unholy mix of science and magic and that the mask is a conduit of some ancient, hellish force that is not specifically named but that has much to do, albeit in the background, with the monsters and demons being there in the first place.
Play-through videos are avaliable at www.youtube.com.
Sources: Wikipedia pages.