I know a lot of families who watch nothing but nature shows, like that Planet Earth series. (God knows what horrors today’s kids are going to face in the years to come. Maybe when they have their own kids they will think back and tell them about what the world used to be like, and the living creatures once in it.)
Don’t they show cartoons any more? Like Bugs Bunny? I suppose it’s too dated. All I see, flipping channels, is musclemen in tights, and robots and stuff.
Oh, I originally came here to suggest The Andy Griffith Show. Again, dated, but one of the best shows ever.
“The best way to a man’s heart”? 
We can hope a kid would take that as a joke.
But how sweet of them to edit the tapes so that Hope can watch, eventually. “My mom gave Osama a swirlie!”
Yeah, ZipperJJ, I do have mixed feelings about letting my 10 year old watch Peep Show with me, but he is mature and smart, and enjoys the sensibility of the humor and the over-the-top bad attitudes and goofiness. We’ve never noticed sex scenes. Maybe they cut them out here? The sexual innuendo and humor goes right over his head, mostly.
My big show to watch with the kids is The Simpsons, although it’s not entirely child-friendly. I enjoy Family Guy and South Park but wouldn’t watch them with my kids.
My wife enjoys reality shows and a couple are family friendly. Master Chef is the one she’s been watching with the eldest. There’s also an Aussie game show, Talking About Your Generation, that she watches with him.
I have a hard time finding shows I like well enough to watch with my wife, let alone the kids. Mythbusters and Dirty Jobs are OK but don’t interest her and I consider them to be missable. There’s one that hasn’t been mentioned but I’m sure heaps of posters watch: Big Bang Theory. There has been a lot of Leonard-gets-laid episodes, though.