We’re just about to finish Dr. Who. (From Eccleston on. We occasionally watch some Classic Who episodes too but that’s not something we’ll probably be working through every episode of.)
What should we do next?
The kids are 9 and 7.
The parents are 36 and 36. 
Hard to go wrong with Firefly.
Dr who came close several times and I think firefly unfortunately crosses the maturity line too deeply for us right now.
I should mention btw we already worked through the various start treks
Twilight Zone. But only at night. The original Battlestar Galectica. Xena and Hercules.
You can check out the movie The Librarian: The Curse of the Judas Chalice. If it passes muster there is a TV series.
Ooops. The Curse of the Judas Chalice is the third and last move of the librarian series. The first two were Quest for the Spear and Return to King Solomon’s Mines.
The Twilight Zone is fun, but I like Alfred Hitchcock Presents better. When I was the OP’s kids age I wasn’t ‘allowed’ to watch it. I think it was a combination of being on at my bedtime and my mom thinking it would be too scary. I remember that I would get to watch the intro music (which I always liked) but then it was bedtime.
Anyways. If they don’t rattle easily, that might be fun. It’s certainly not that scary, it’s like a little 20 minute mystery to solve. It’s also kind of neat to see them recycle actors.
Another one, if they can appreciate the comedy, is Fawlty Towers.
Avatar: The Last Airbender
The 10th Kingdom was cute. It’s a miniseries from 2000. Has some PG moments. The 10th Kingdom (TV Mini Series 2000) - IMDb
Maybe The Adventures of Merlin? I didn’t actually watch that one.
The Simpsons, Adventure Time, and My Little Pony: Friendship is Magic are all shows I know kids will watch that I also find interesting.
Stargate SG-1 is a personal favorite but some episodes are perhaps a bit too adult for kids. Richard Dean Anderson does display a comic touch that I think kids would enjoy.
Babylon 5 is rather melodramatic and geeky, but those qualities may actually make it seem cool to kids. If they liked Star Trek they’ll probably respond to Walter Koenig’s recurring role (he played Checkov in TOS).
When do they get to watch ATHF?
You could watch series 1 and 2 (possibly 3) of Buffy. Later seasons get too adult, but there’s enough in there to keep you all entertained.
Futurama might be something that they’d love, wouldn’t drive you mad and does actually have a storyline. The new series of Scooby Doo is also more grown-up than the earlier series, so better for the adults watching but still entertaining for the kids. They might be watching both of those already out of sequence, though.
If you and they liked Dr Who, they might like The Sarah Jane Adventures, which is a spin-off of Dr Who aimed at kids, but not babyish.
I was about to suggest both of those. Excellent series to watch with kids.
Ceee-ee-ties of Gooold!
I might have been a little older than 7-9, but my brother and I used to LOVE Quantum Leap.
Seconding (or whatever) Avatar. Also Babylon 5.
The Avengers: Earth’s Mightiest Heroes, a cartoon on the Disney channel, is also pretty good. Not top rate, by any means, but enjoyable, with some occasional flashes of real quality.
Batman: The Animated Series will stand the test of time, as will much of the rest of the Bruce Timm DC Universe - if you’re interested in going down the animated route. If not, Smallville is decent for live action television Superman.
Chuck is good, but may have some mature moments to avoid.
This, absolutely. The ages are good for it.
Edit: make sure it is the TV series and NOT the live action movie! This is very important.
What about the original Hitchhiker’s Guide to the Galaxy? I have both series on the same dvd package, and the wife and I just watched it again last night. It’s not normally something I’d recommend to kids that young, but if they like Dr. Who go for it.
I’d also highly recommend the animated The Tick. There’s only 3 seasons, but it is hilarious. It parodies the superhero genre but doesn’t (IIRC) contain anything inappropriate for younger kids. I have the first 2 seasons on dvd, not sure if the 3rd one is out. Don’t bother with the live action one starring David Puddy from Seinfeld, it’s garbage.