Second comment nailed it. Games are escapism from our normal daily nonsense. A game fails when it can't take us away an immerse us in other worlds.
But, to stick to the actual idea, I'll go ahead and say minecraft comes immediately to mind, with it's interminable creativity and ways to shape the world. Infamous and Arkham Asylum had my subconscious planting me in those roles whenever I wasn't conscious. Skyrim made me want to build things with hammers and power them with magic and thu'um. Saint's Row, Mafia 2, Just Cause, GTA, and a few others make me hate seeing people crossing the road anywhere but crosswalks, because my mind is not conditioned to think of them as targets to aim for; ditto cars I want that pass me on the road--I want to catch up to them, jump from car to car, and yoink it for the garage I don't have.
All of these things are better than my life. My life is dull and boring most of the time, and I'm the kind of person who takes advantage of open plains and cheap planes to go skydiving, or to travel to the Florida Keys to go SCUBA diving. But I'm limited by my form. In games, I'm the perfect genetic result of combining adventurers, gymnasts, olympians, marathon runners, crack-shots, and free-climbers. I can run and jump and climb on everything, or be totally silent while I bow-hunt lions and tigers and bears (oh my), any and all of which would maul me dead in real life, or run the hell away if they didn't want to play with their food.
Even driving games are better than real life. I can't count how many mounds of dirt or cargo trucks with the ramp down that I've wanted to launch off of, or how many times I wish I could just let my car absorb the damage as I plow through traffic. This is, after all, exactly what they're for.