I like violent videogames, but only if the violence is within reason and if it actually makes sense in the type of game it is in.
Basically, what I mean by that is that I enjoy games that involve violence. I have played Prototype where I slashed appart thousands, and I have played Half-Life 2, where I took down hundreds of Combine soldires. I think these kinds of games are fun, but I do know that there are some occasions where the violence reaches that point that it might be too unnecessary (I am not referring to these games). I cannot think of any real good examples off the top of my head, but my meaning is that while a game can have blood and gore in it, the blood and gore cannot be the only thing the game has going for it. If I am ripping peoples heads off every minute or so, sure it may be fun at first to be able to do that type of thing, but after a while it may seem repeated, and somewhat silly. For any type of thing to have a meaningful effect - violence in videogames included - there has to be some sort of pacing, where the violent moments acutally hold some weight. Otherwise, the violence loses its importance and hold, and the game no longer has any serious meaning to it, other than a game that you occasionally play to blow off some steam.
The other point I made is that the violence has to have a reason to be there. There are some games where punching a person's head clean off makes sense, and there are games where anything more than a comical slap seems over the top. Games are different depending on the subject and nature, and the violence needs to be adjusted accordingly. In a game like Mario, or Pac-Man, unless the goal is to make a gritty reboot of the series like "There Will Be Brawl," adding blood and guts to the game would not improve it. In fact, making either of those two games more violent than what they really are will turn me away from them. On the other hand, the main God of War trilogy of games has very violent situations. In the third game you tear off Helios' head and use it as a flashlight. However, the game trilogy revolves around Kratos, the killer and eventual God of War. The game is about a man trying to get revenge and redemption. It is about a man getting angry and willing to destroy the world just to try and carry out his anger. In that game violence makes sense, and it would be ridiculous not to have violence. Looney Tunes: Back in Action was a game about the Looney Tunes movie of the same name. Looney Tunes is meant to be the kids' cartoon show. Violence would have made the game inappropriate for the younger audiances, and would feel out of place in a cartoon world. Constantine - a game based on the movie of the same name, based on the comic series Hellblazer - is about a chain smoking American (English in comics) who fights demons from Hell. It makes sense to have violence in a game where evil demons from Hell come to Earth and kill people.
Basically, I like violent videogames, but only if it makes sense in the context of the game, and if the violence is not pushed too hard. Otherwise, the violence becomes silly and out of place. Violence does have its place in gameing, but only if it drives a story or is used with pacing. I do not think you can have a whole game with nothing but violence, unless of course it is a very short game - the type you occasionally find online, and play after you had a really bad day.