Jeopardy?
My vote is for Sherlock. So dazzling and brilliant. The way that it somehow manages to simultaneously tell the original stories and be a contemporary show, while tossing off all sorts of arcane references and being hysterically funny just leaves me in awe.
I’m currently watching a season of Quincy on DVD, and I’m very impressed. Just when I think that they are telling a cliche story, there’s a really smart and interesting twist.
Justified. Almost any of the dialog spoken by the character Boyd Crowder.
I was always surprised by how many out-of-the-way references 30 Rock had. I guess since they had such a high joke-per-minute rate, the producers were less concerned that some stuff might go over some peoples heads.
The original CSI and the first few years of CSI: New York.
Meeting of Minds, yes!
On BBC, Mastermind.
Second both Frasier and DvD. I’ll add Cheers! to the mix.
St Elsewhere.
If Jeopardy! is eligible, then so is the original Split Second, with Tom Kennedy. That show moved so fast and the contestants were so damned smart, I was always left in a blur when each episode was over.
It may seem old hat now, but I still love watching Columbo, even though I know each episode by heart and exactly how the murderer is going to give him/herself away. But I always think of when I saw them for the first time and wondered “How on Earth is he gonna nail him/her???”
I would say SCTV, for the way it assumed the viewer had a wide knowledge of pop culture marginalia, plus an appreciation of how to reinterpret such material with irony.
Mary Hartman, Mary Hartman struck me as a pretty brainy show as well. Also for its irony, and the ambiguity of its dialogue.
I think when it gets into the semi-final and final stages, Only Connect has some of the toughest questions I have ever seen in a TV quiz. Things like *Mastermind * are about testing your memory and general knowledge. Only Connect needs general knowledge and actual reasoning and lateral thinking. Of course, that doesn’t make it brainy in the way a well-written serious drama is, but yeah, as entertainment shows go it must be up there.
What about the much branier (but short lived) Never Mind The Full Stops
I would nominate Mystery Science Theatre 3000 - MST had quick, witty writing, wasn’t afraid of obscure jokes, and to catch all of them (or even most of them), you needed deep cultural literacy, knowledge of previous episodes, and often a strong base in science, religion and philosophy. They would make a Proust joke one minute, then a joke about apes throwing their poo the next.
Settle down, Howard! 
The West Wing deserves a mention. Even if you don’t agree with the politics, you have to concede it was smart articulate characters dealing with important issues.
The BBC series, Yes, Minister.
The first thing you had to get past was that Jayne Meadows seemed to play every important woman in history.
Sherlock
Sopranos
Carnivale
Breaking Bad
Boardwalk Empire
Frasier & Cheers
NYPD Blue
*agreed on Monty Python’s Flying Circus
and…I think South Park!
p.s. The Dick Cavett Show
oops, I forgot The Twilight Zone.
I will boringly nominate the first 15 years of The Simpsons. Any show which can so easily appeal to adults and children, smart folks as well as dumb folks is working on a higher plain than almost any other series.