I never put it on intentionally but I can still watch friends without being completely bored (seen every episode multiple times for multiple reasons) *waits for the abuse*
I've seen every episode of Friends, Frasier, and Seinfeld. All of them are shown daily so I'll frequently re-watch episodes if nothing else is on or if I want something on in the background that I'm familiar with. These are all comfort shows for me, particularly Frasier. Frasier also has the best TV times for me. There are repeats from 8:30am-11:00am every weekday morning, so that gives me something I could put on when I wake up. On a different channel there are daily repeats from 3:00am-5:00am, which is a sweet time because there often isn't anything better on then.
I rewatch King of the Hill as well because of this same reason. It has repeats on from 5am-6am on Cartoon Network, so if I happen to be awake during those hours I have something to watch, especially since there's rarely anything on aside from infomercials after 5am.
Other shows:
The Wire and Breaking Bad because they are just fun to go through. Even when you know what's going to happen there is still so much to every show that it's easy to pick up on things that you may have missed or foreshadowing that wouldn't have been picked up on an initial view. I've already seen every episode of each show 2-3 times, if not more, but I would still rewatch them both.
Mad Men - Gotta love Don Draper and crew. Hopefully the last season lives up to the first 6.
The Sopranos - Fun to rewatch and go through again, though I've never actually seen season 6.
Arrested Development - same reasons as other shows, but because of hilarity and it's incredible depth.
The Simpsons - the first 10 seasons were hilarious. It takes me back to growing up, but the show is still funny to me as an adult. Because of the frequent daily viewings I had growing up I still quote it quite often. I'm tickled pink whenever someone actually picks up on a reference. My senior quote in my high school year book was "I wash myself with a rag on a stick"
30 Rock - Similar reasons, plus there's repeats on daily. Still haven't seen the last season though.
The Office - Same as 30 Rock, but I still haven't seen the last few episodes of the last season. I don't know if I'd watch the repeats of Season 8 and 9. They really seemed to go downhill there.