I do it on a first playthrough for RPGs, simply because I want to see what problems (or steamy romantic escapades) my own idiocy will cause. BIG mistake in Mass Effect doing that, as I'm sure other people can attest to. After I beat it I was pretty mentally messed up for like a week and a half.
Other games though, I don't tend to self-insert, and more like, allow them to be inserted into me (OH MY GOD), as in like, I like to think that the character I'm playing is telling me a story to teach me a lesson or something, so I can become more like them (usually heroic.) In the Sims for example, I never make myself, but after playing for a while I feel like the character is me and I am them. Although I do find it hard to do that with male characters at all, so maybe there is still some subliminal stuff.
I really need to work on my words.