It's too easy - if you want to start a fight, make a list.
Cullen's right, this thing is borderline silly. Any list will leave shows off: either shows not seen or shows that (fairly or not) the individual in question simply hates. For what it's worth, I'd set my top ten brainy shows up roughly like this - with the caveat that these are shows I've seen a lot of. If one you prefer is left off, it's probably because it's before my time. And all other things being equal, I went with the more entertaining show over smart and dull, because you have to be pretty smart to be able to entertain with a smart show.
Jeopardy - you can't simply guess your way through this board. Bonus points for having two famous hosts AND a Wierd Al parody song. (Which makes sense how, exactly? I dunno. It makes sense to me. I won't hear any more of these ridiculous accusations!)
The Simpsons - with all due respect to the excellent Futurama, the Simpsons is the cleverer show. The song work is incredible; the quick sight gags and word plays never overwhelm the characters or plots; and it's lasted forever. To be that seriously good for so long really takes some brains.
Bones - I prefer this to the various CSI franchises. They debate a lot of really heady stuff while they solve crimes, and very little of it seems forced - that's some good writing (and great acting).
Mythbusters - any show that blows stuff up for SCIENCE! has to garner some consideration, the moreso because they are informative and entertaining at the same time. Along the same lines (but not as "smart") was Junkyard Wars - they didn't do as good a job at explaining some of the principles behind their actions because of the format involved.
Good Eats - a nerd show about food. The concept itself is just genius, but to pull it off takes some brains, not the least of which belongs to host Alton Brown. It's not just about yummy food but about why it's yummy, and how the recipes work the way they do.
Sesame Street - it isn't easy to get kids to learn, but they do it, primarily by not assuming that kids are dumb just because they're innocent and little. Always catchy and inventive.
Schoolhouse Rock - you could say that these three-minute snippets weren't shows, per se, but stop for a moment and think about it. Do you know the preamble to the US Constitution? The times tables? How do conjunctions function? Or the nervous system? And all of it set to extremely well-written jazz, funk, pop, and country. That takes some kind of genius.
Mystery Science Theater 3000 - from concept to execution, this remains one of the best shows ever. They were smart enough to withhold explaining WHY the show happened: the theme song set it up and then you were off. Bonus points for the invention exchange segments, which had to be discontinued after Joel Hodgson left, since he was the guy who came up with all of them. (This is not to dig Mike Nelson, who was after all the show's primary writer.) Above all, the basic likeability of the poor guy in space gave the show charm to go along with its wit.
The various WB Batman/Superman animated shows - maybe this list really betrays what kind of schlock I grew up with, but I stand by the choice. Leaving aside the Justice League and Teen Titans stuff, just focus on the two shows where Bats and Supes went solo. You've got excellent voice work all around (especially the leads, Kevin Conroy and Tim Daly), fine plots, and a focus not just on the derring-do but on the alter-egos and their problems, most of which can't be solved with a timely kick to the chops. I especially like how these shows let you into the thinking aspects of each character as they faced their challenges.
I'm going to make those last two shows #9 and 10. They're not in any sort of order, you'll see. I'm not smart enough for that. And I'm going to go ahead and apologize in particular for two programs: MacGuyver and Quantum Leap. Wonderful shows, and very cleverly done, but I haven't seen more than three or four of each of them, so I can't put them into my own list. If you guys want to do something less, you know, cartoony, then by all means swap them in for two others. (And geez, there are an awful lot of cartoons up there. And musical stuff. Heh, drawing and singing, two things I really don't do well, wind up all over the list - that's not connected AT ALL to ANYTHING.)