I agree totally! The viola (I thought it was a cello) was what gave you the gothic underworld feel that said “Here comes a darkness dwelling vampire to kick ass and chew bubble gum!”
The full orchestra version said: “Here comes a super-hero!” I thought it was key to the character of Angel that he wrestled with his inner demon and redemption above and beyond was his goal. If he’s just a plain old super-hero, it’s not the same.
I liked how the narration of the Farscape opening (slightly) reflected what was going on with general development.
There was an episode of Monk mildly spoofing cop shows–Mr. Monk was called to the set of one of them. I think Sarah Sliverman was in it, but I’m not sure I’m remembering that right. Anyway, someone was playing something of a stalker who was pretty pissed that her favorite show had changed the theme. Now, whenever we hear new themes to shows Mrs. Devil and I turn to each other and snark “now, why would they go and change a *perfectly *good thing?!” We’re not all that huge Monk fans (hence my poor recollection of the episode), but that stuck with us. Fun.
(Any corrections to the above are welcome.)
ETA:
heh… just plunked a bit in and found it. Fun trivia from IMDB
Actually, it had three openings. The first season or two the opening consisted of a series of still photos presented in sequence – no Rob entering a room, and no hassock at all.
When Get Smart moved to a new network, they changed the beginning of the sequence, although the walk down the hallway with the doors was the same.
Hey, thinking of doorways – the sequence of doorways in Mystery Science Theater was filmed three different ways. (Four if you count the movie.) And they changed the entire opening (except the song, with minor changes) every time there was a change in venue or cast.
And now I love you a little more! 
You are probably right - it is a cello. All I know is that it was the best part of the theme music.
Numb3rs had at least 3 main titles. The original had Charlie talk about the use of numbers in everyday life over the groove of Talking Heads Once in a Lifetime. Now it’s basically a fade to black. I’m pretty sure that there was one other.
There was an episode of Family Guy where they did the opening in Law & Order style.
So did Sex and the City.
Any show that’s on long enough will change the opening – to account for cast changes, or just for variation. MAS*H changed scenes with cast changes (in addition to changing the names). the Simpsons changed the opening recently, and every opening has differences in Bart’s chalkboard writing, the Couch Gag, and (I think) Lisa’s solo. They occasionally throw in other changes, too (like the live-action version, or the post-movuie version, or the recent one where all the band members are texting instead of playing their instruments.)
petticoat Junction changed its opening in minor ways a couple of times, with Bea Benaderet’s death and with different numbers of dresses o the watertower.
the Life and Loves of Dobie Gillis changed when it became Dobie.
That Girl! changed, getting a new “logo” when Anne Marie got rid of her bangs.
All in the Family re-recorded the opening to make the line “…Gee, our old La Salle Ran Great…” more comprehensible.
[Yul Brynner] et cetera et cetera et cetera [/Yul Brynner]
Star Trek added DeForrest Kelley’s name to the opening credits in season 2 or 3.
Deep Space Nine had to rearrange names when Siddig el-Fadil started going by Alexander Siddig. I’ve heard he did it because he wanted his name to be next to Nana (Mrs. Alexander Siddig) Visitor’s in the credits.
Early episodes of WKRP in Cincinnati have a intro where someone is tuning across the AM dial before “finding” the opening notes of the theme song.
Remington Steele’s opening credits changed drastically from season 1 to season 2, then again in season 3, then much less noticeably in season 4. Season 1’s, with Laura’s voiceover, were the best.
Quantum Leap’s credits changed slightly every season, with montage shots from different episodes.
I believe the narration was dropped in the first season.
And Max’s car got increasingly lamer - from a Sunbeam Tiger in Season 1, to an Opel GT in Season 2, to a Kharman Ghia in Season 3.
Originally, I Dream of Jeannie had a filmed opening with narration of how Tony found Jeannie’s bottle and they moved to a mythical place called Cocoa Beach. I think the animated opening began in Season 2.
My favorite was the Caribbean flavored one.
Several used the same theme but updated the images a bit like Dallas and Friends. The Bradys went from 60s shortcuts to man-perms for example.
Hmm, I bet a lot of these changes in opening themes are misremembered. We need a more accurate assessment method.
Y’know… a thematic perception test.
“…but the Senator, while insisting he was not intoxicated, could not explain his nudity…”
Bewitched cartoon intro for York or Sargent
I thought most shows did this.
Anyhow, I’ll add Lavergne and Shirley. There’s a few differences in the first few seasons, but once they go off to Hollywood, it’s a totally different sequence.
Good Times has a number of different openings. The early ones have prolonged footage of Cabrini Green in the opening, later ones have more cast member footage.
Facts of Life also changed it up frequently. The first season’s opening song even had slightly different lyrics and was a different recording of the theme song we all know. Instead of “You take the good, you take the bad…” the lyrics started “There’s a place you gotta go for learning all you oughtta know…” See here. If you look to the right, you’ll see links for slews of different openings.
Since the OP spoke of Gilligan’s Island, it may be interesting to note that the original theme song (only used for the pilot–I’m not sure if it aired or not) was completely different.
And there’s slews and slews more. I have a friend who collects various intro sequences for TV programs and I’d guess the majority of them change up their sequence from time to time. Some as often as every season.
If you want to tinkle with laughter. first check out the Season 1 version of Baywatch Nights with David Hasselhoff being as Magnum P.I./Miami Vice as possible… and then…
Hoo-boy!
The werewolf-ghost-chasy-monter-hunter-Hallowe’eny Season 2 “The nights will never be the same!” Baywatch Nights.
ETA: Added bonus, Hasseloff sings the theme.
The opening to The X-Files for season nine is completely different than the opening for seasons one through eight.