Must second It Takes a Thief
Green Acres( summed it all up)
Wild Wild West
Super Chicken and/or George of the Jungle and/or Tom Slick
I honestly don’t think you can beat…
“THIS…is the city: Los Angeles California.” and then a brief description of LA or the inhabitants or the society leading into ‘I carry a badge.’
Dragnet was great. Jack Webb NAILED that role.
I’ll vote for Gilligan’s Island, simply because of the succinct and entertaining way in which it summarized the show’s premise.
Aqua Teen Hunger Force is up there. “Shake-Zula, the Mike ruler…” It’s hard to beat that.
I have to say that I love the Arrested Development theme music. It’s so perfect.
I always loved the cheesy montage opening of The X-Files. That was a great theme song, too.
How about Get Smart? Or The Simpsons?
A very honorable mention has to go to The Muppet Show. (Season one coming to dvd very soon!) With the unique cuts to Stadler & Waldorf for each episode…that opening was classy & classic.
I was raised in Northern New Jersey, and the opening to The Sopranos just makes me giggle every time. I mean, Pizza Land in Kearny, for crying out loud. That aside, I think it’s oddly effective for setting the tone of the series without giving anything away but its essential Jerseyness.
Fat Albert
A-Team was cool as hell too.
A hearty second for Battlestar Galactica. I loved that melancholy music playing over scenes from the miniseries, showing the near-complete destruction of humanity. My favorite shot is the new President being sworn in on her ship (echoes of Lyndon Johnson), looking deeply stunned.
For the reasons Malodorous gives above, I’ve always kinda liked the opening for Dharma & Greg. About 10 seconds long, kinda sweet, gives you a quick glimpse of what the show is about, and that’s it. No more than is necessary.
Northern Exposure. The funky song, the various shots of the town and the moose, with a couple shots of it looking contentedly into the camera always made me laugh.
“Snowmobiles, $1500, Xlent Cond.” 
Batman: TAS hands down. It gave me shivers at 4:30 PM in the afternoon.
Honorable mentions: Rurouni Kenshin. Images of our favorite characters doing their thing while that catchy bubblegum music plays. Samuari Jack for the same reason. Well, not bubblegum musc, but catchy.
You tell 'em. Perky, atmospheric and with a bit of variation/humour with the messages.
The Simpsons For the first hundred times you saw it. Now it’s just the cue to turn over (like the Archers theme).
For kids shows I’d say any one of three Gerry Anderson shows:
Stingray – Anything can happen it the next half hour!
Thunderbirds – are GO!
UFO Already mentioned in the OP (the closing credits were proper creepy too).
I’ve said it before, and I’ll say it again - Jack of All Trades.
Also, Greg the Bunny.
I like the new opening for Alias - the montage of many of the fabulous outfits and disguises Sydney has worn.
“Gargoyles” - The opening has catchy music, explains the important parts of the backstory, and is surprisingly dark for a cartoon.
“MacGuyver” - It’s been years since I’ve seen the show, but I can still remember the music and the montage of narrow escapes.
“The Sopranos” - Not really sure why, except that it has terrific (and very fitting) music and I love the view of Tony heading from the big city back to Jersey, and pulling into a nice suburban home.
Doctor Who: Jon Pertwee’s final season, the recent series, and Tom Baker seasons 1-6 in that order.
Star Trek: TOS
It’s GOT to have a great theme song …
The Best:
The Prisoner
Pretty Darn Good:
Cimarron Strip
Deadwood
Deep Space 9
Men From Shiloh
Cheers
The Avengers
Star Trek: Voyager
I really enjoyed the opening of the mini-series “Kingdom Hospital.”
I hope it gets rerun some time with a schedule that doesn’t bounce all around and disappear for long periods.
If they did nothing but show the opening sequence over and over again, it would have been a good series!
I agree, though, the opening theme was, IMO, the best of all Treks.
I also think Babylon 5 seasons 3 and 5, and even 4, where all very good. Season 5 might be the best, because it contains my all-time favorite B5 line:
Sheridan: Now get the Hell out of our galaxy!
Star Trek: Voyager
Best animated openning?
For my money it will always be:
Jonny Quest