I have no one favourite game, so I'll just list my top favourites and what I'd do:
Thief Series: Join the Mechanist Order. Now, I wouldn't want to be there after it falls, but at the same time, Karras was planning to betray even his own followers... so I'd probably find a way to sabotage Karras' plans WITHOUT causing the fall of the Mechanist Order. Best way might be revealing his plans to the other Mechanists, if I could gather some solid proof. Then we'd be able to get a more reasonable leader. Since the Keepers would no doubt be interfering with things, the Pagans would eventually recover their strength and an overall balance would be kept.
Also, I'd take a group of Builder's Children and demolish the Shalebridge Cradle. I hate that place.
Mass Effect: Well, as a civilian, my options would be limited. Still, it'd be preferable to living in the current day. Might join the Alliance military anyways.
Dawn of War series: Die, most likely. It's Warhammer 40,000, and I'm an ordinary human.
Gears of War series: Again, I'd probably die. GoW is pretty much 40k on one planet anyways.