Yes I do actually. Usually after I've forgotten the details of the plot. With Bethesda games I replay them sometimes after a year when all the DLC has come out =), I usually do a different type of character.
Some games however I replay immediatly, usually on a higher difficulty: Dead Space 2 comes to mindn or DMC 4. The first 2 Mass Effect games I have replayed 2 times, a male paragon shephard and a female renegade shephard, but i have yet to start the third. I don't care about what everybody said, not playing a game because of 5 minutes of ending that might not be what I expected isn't really in my mindset.
I'm currently replaying Red Dead Redemption, because I like the plotline and I appearently forgot a lot of things on my first playthrough.