I did. In fact, I remember playing GTA III when I was only 12, and DOOM, Goldeneye, Mortal Kombat, Turok etc. before it.
My mom was actually pretty strict when I was younger too (not at all anymore), so I'm actually surprised she didn't stop me from playing violent video games. To be fair, at the time I don't think she really understood video games. And just assumed...they were "games".
Then again, I was also heavily into Tarantino at the age of 13. So maybe my mother was always more laid back when it came to media violence. Truth be told, I had really great parents that taught me love and kindness (not to sound cheesy) before anything else. I think that made me a really well rounded person to begin with, and so the media stuff was just entertaining and cool to me. An afterthought that had no influence on my attitude or behavior.
Just my experience. But I can honestly say games haven't had a huge impact on me at all, in terms of how I act, and the things that I do. Same with film. At best, they just helped define my taste in entertainment.