Anyone can name dozens of sitcoms they’ve never watched; some come and go so fast that you never even realize they’re on.
I can’t say I never watched a lot of the successful shows, but there are plenty I’ve never watched an entire episode of. These include:
Full House
Boy Meets World
Home Improvement
Everyone Loves Raymond (I sample this from time to time, but if I watch more than 5 minutes, I get violently ill. Probably the most offensive stereotyping currently on network TV.)
The first one I missed was “Leave It To Beaver”, I don’t know for sure, but I think I was going to college at the time and back then no one I knew had a TV at school.
The two that I’m proudest about missing are The Simpsons and that show with the fat gal that screwed up singing The Star Spangled Banner. 
I resent the inclusion of Gilmore Girls in that group.
Reading this thread, I realize I have a problem. I can’t think of a single show I haven’t sat through at least fifteen minutes of.
I have seen at least one-half of one episode of all the shows mentioned except the recent premium cable shows (6 Ft Under, Sopranos, etc).
I have also seen AKA Pablo (I think I saw the entire run. When I was a kid, I thought that Paul Rodriguez’ schtick was the funniest sh*t. I was half right.).
I have seen She’s The Sheriff.
I have seen Three’s a Crowd.
I have even sat through an entire episode of Small Wonder.
God help me, I even saw the entire 20-some-odd episode original run of “What a Country”, Yakov Smirnoff’s syndicated sitcom from the mid-80s.
Memories . . . flooding back . . . into brain . . . Oh, the pain . . .
::curls in a fetal position, whimpering to self::
Well, the OP said sitcoms but that’s been ignored, so I will chime in here with the fact that I have never seen two consecutive minutes of The X-Files. And I’m a sci-fi geek. Also:
Wrong again. I’ve never seen that or any of the other reality shows.
I have never watched a reality show. I saw thirty seconds of Survivor once by accident, but that was it.
I have never seen ANYTHING that’s been broadcast on UPN or the WB (including Buffy, for which my brother’s always needling me).
The only prime-time drama I have watched in the last ten years is ER, and I don’t watch it any more. And a few episodes of The West Wing, but, as a Republican, that show just irritates me. I’ve never seen Law & Order or any of its relatives, The Practice, Third Watch and much, much more (I have seen Boston Public, but only occasionally).
I skipped the entire runs of Home Improvement, Married with Children, and Growing Pains.
I did, however, love the shortlived sitcoms Cafe Americain with Valerie Bertinelli and Jennifer Slept Here with Jill…help me out here… I have seen The Simpsons, though not dedicately (my hubby hates it). I have reluctantly watched a number of SciFi shows (which my hubby enjoys), but I don’t like them. I just don’t care enough about TV to plan when I’m going to watch, so I miss a lot of continuity.