The soundtrack to that is on my playlist.
Animaniacs. Sorry for being infantile 
Battlestar: Galactica, the new series. I love that opening song and then it goes into those drums. I watched the entire series on DVD and never once fast forwarded through the credits.
Get Smart
The Prisoner (sorry, no link at work) had good ones, describing the premise concisely with excellent music. Perhaps the most quoted opening credits “by hook or by crook, we will.”
Some are non-standard. My favorite was Green Acres. In one,the credits were written on eggs which Eva Gabor collected at the beginning of the show - and she of course noticed the credits.
Rome is the only series where I looked forward to the opening credits.
As a kid I would have said F-Troop and Get Smart as well.
The BSG remake I liked for the first season, then started fast-forwarding through.
Seconded!
How about:
Simon & Simon
The A-Team
and of course The Dukes of Hazzard
no links at work either.
Folks, don’t forget Mission: Impossible.
Also, Sanford and Son.
Shut down this thread, I have the winner…
♫ Now this is the story all about how my life got flipped-turned upside down… ♫
I don’t particularly like the new version of the show, but I do like the new credits for Shameless
No, you’re not being infantile! I’ll stamp my feet & start screaming if anybody says so!
Love Twin Peaks for the atmosphere it set. And, although I didn’t love Star Trek Voyager, the opening credits were beautiful. (The visuals for the* Enterprise* opening credits were fine; the song sucked.)
Oh, look! SFX has a list of “special” opening credits.
That’s the one part of Firefly that isn’t brilliant. In fact, it’s the worst part of the show.
This had it all…and bongos!
The opening credits to Crime Story rocked - literally!
Garry Shandling keepin’ in simple.
Champion The Wonder Horse
Moonlighting
Now And Again
Action
Oh, and Peyton Place
Seems to me like everyone in the US would recognize the theme to The Andy Griffith Show.
The High Chapparal
White Horses
The Lone Ranger
Follyfoot
and the best EVAH… Tales Of The Unexpected
Hawaii!
Mustaches!
Swoopy Helicopters!
Underwater SCUBA Fighting!
Larry Manetti!
Magnum P.I.!
I have 2 favorite tv show opens: Dr Who and Medium. In both cases, excellent music.