Some well written games or memorable characters affect me in the same way as any other storytelling would. I can't really gauge how much, but fiction in general doesn't affect to the point of obsession or anything like that. I might find a nugget of wisdom or inspiration here and there, and those will stick with me.
The mechanics behind games probably affect me in positive ways. Most games are basically just...pattern recognition. I'm sure that helps on some level, like a mental exercise or something.
I've mostly played platformers/racers/RPGs/adventure titles...as far as storylines go, most of the themes are Japanese or western fantasy/sci-fi based. I'm bored by military shit (including movies) and most of the FPS genre..nor do I care to be, like, some psychopathic ghetto character in South Central LA.. so I don't think I play enough games with gratuitious violence to affect me negatively even subconsciously.
edit: Wait, the Metal Gear series is badass..but then, it's kind of an anti-war game (and in MGS4, even a commentary on the negative influence of war games)