Yes and no. Violent games were never an issue. I mean, at age 5 or so, I was playing Doom/Quake 1. Evil games (ones where you get to play an evil role, that is)? Slightly. By which I mean I remember my mother getting a little panicked after seeing the cover to the Dungeon Keeper box, with a tagline to the effect of "evil is good". Understandable, given my young age at the time, though it didn't affect me or anything.
These days? Not in the least. Though I remember that my father cared a lot about quality back when I was younger, and I mostly wound up playing PC games he had finished with and recommended. This meant growing up on Sacrifice, Infinity Engine games, Half-Life and some other stuff. And, yes, the aforementioned Dungeon Keeper.
My younger sister, meanwhile, was utterly convinced that games were stupid. Unless they're Diablo, or Heroes of Might and Magic 3. Those are great. I'm not sure how that happened, why those two, or anything like that, though. But I do remember getting Diablo when it was released. Needless to say, I was very, very young then.
So all in all, I'm quite grateful for the little monitoring I did get.