when I was really little, it was mega man, and mario.
Then when I hit about 9 or 10, Mortal Kombat 3 came out, and I got that for the SNES, and my mom made me return it.
at about the same time, I got Diablo for the PC (which I LOVED), but my mom made me return that as well.
3 years later or so, I was playing a LOT of Warcraft 2, Starcraft, Diablo (yes I got Diablo again a couple years after having to return it.. I don't even think my mom knew that she let me have a game that she had banned, but I loved it so I wasn't going to say anything).. Some Quake as well (Primarily Team Fortress and Future Versus Fantasy)
(If you're interested, as late as 2006 people were still playing FvF, which is one of those mods that DIDN'T get picked up, but was a HUGE fan favorite of the Quake Modding scene - http://fvfonline.com/#info)
Once I was about 14, my parent's censoring wasn't an issue anymore, so I could play with whatever I was. So to answer the topic's question, from about the age of 10, I tipped my toes into violent games, and by the age of 14, I played mostly violent games.. now I play pretty much anything.