If they ever reboot Barney Miller, it won’t be the same.
For one season, they dropped the entire opening of Bart writing on the blackboard and everyone coming home to the couch.
Wasn’t the “World Turning” intro used for a while? Or was it just a one-off work of brilliance?
All In The Family had four versions:
Season 1: Recorded in front of a live audience.
Seasons 2-5: Audience is gone, the camera is at a slight angle, and Edith is wearing reading glasses.
Seasons 6-8: Archie and Edith are shot from straight ahead, Edith’s glasses are gone, and Archie is noticeably heavier.
Season 9: Archie is wearing a sweater, Edith really hams it up on the line “And you knew where you weeerrrrreeeeee then,” and Archie drags out the line “welfare state.”
The closing credits for the final season were re-recorded with a clunkier arrangement and Carroll O’Connor replaces Rob Reiner’s voiceover.
By John Williams, who must have been coming off a bender.
“Night Gallery” had three versions; version 2 was slightly different than version 1, but version 3 was way diff.
Futurama followed in the footsteps of The Simpsons: They would show a short clip from a different classic cartoon on a giant TV screen each episode.
Bob’s Burgers has a different (punny) business name in the store on the right, and a different (punny) name on the exterminator’s truck. Not in the credits, but they have a different (punny) burger of the day in each episode (sometimes two if the episode goes on for more than one day).
Perhaps not massive, but significant.
In the opening credits for the first season of the Mary Tyler Moore show, Mary Richards is shown leaving her small-town home and driving to Minneapolis under the original version of her theme song, which begins with a timid “How will you make it on your own? This world is awfully big and, girl, this time you’re on your own…” and concludes with a hopeful “You might just make it after all”.
In subsequent seasons, but there’s a new version of the theme song–the one that begins with “Who can turn the world on with her smile?” and ends with the confident “You’re gonna make it after all!”
The clips in the opening credit sequences change each year.
“Land of the Giants,” two seasons, two different opening credits with two different songs (though somewhat similar.)
(I would have linked the YouTube clips I saw, but they’ve been doctored to exclude the cast. 
)
That was a one-off, and an excellent one at that.
Which is actually kind of crazy, because the amount of effort that went into editing that sequence in the pre-digital era is significant. The frames had to be selected and cut by hand, and unlike a pre-episode “clip preview” had to be timed to fit exactly with the title music. Given that and the number of sets that had to be made for every show (although there is significant reuse in later series) must have made that show very expensive to produce for its time.
They’ve also played around with the opening credits a couple times each in S2 and S3. And the opening number is composed to foreshadow the overarching plot of each season on multiple levels. The overall amount of foreshadowing, lampshading, and general medium awareness of this show is actually really impressive. Second to the prematurely cancelled Wonderfalls and the always surpsing Archer, it is really one of the smartest and expectation-subverting shows on television.
Stranger
The first season of Space 1999 did this as well. Must be a Martin Landau thing.
The 6th season of “77 Sunset Strip” when Jack Webb became director at tv programming at Warner Brothers. “77 Sunset Strip” was the only Warner Brothers show left (a year earlier there were eight) and it was running out of steam. So Webb fired all cast members except Efrem Zimbalist Jr, dumped the jazzy toe tapping song and the office was moved to a different location. He opened with a five part episode (“Lassie” was the only show previously that had a five episode arc) involving Nazi treasure and on each episode the guest stars (there were a total of 27) introduced themselves. Didn’t work, Webb could only get one show “No Time for Sergeants” on the air for one year and Webb soon lost his $150,000 a year for three years contract (but he got a nice buyout package).
Here’s the original opening theme of Magnum P.I. It changed to the other one after the first few episodes.
The first season or two of Grey’s Anatomy had a full on credit sequence with a cheesy vocal song and “ooh, sexxay high heels parked next to doctor stuff teehee” graphics but that got dropped fairly quickly and now it has no credit sequence at all or theme music, just a quick title card after the cold open and the original cheesy theme song is reduced to an instrumental clip over the end credits.
Oh, and I guess the makers of House MD got tired of paying royalties to Massive Attack because after a couple seasons they stopped using “Teardrop” for the theme music and switched it with the inferior ending credit music instead.
Excuse me? If you are thinking of the episodes where they go straight from the title to an outside shot of the house, that was only for two episodes in the first season. However, the other 10 episodes (besides the Christmas special) that season had an opening that was a little different from the one in later seasons; when Bart rides by on his skateboard, rather than passing some of the regular characters, he grabs a bus stop sign, and then a bus goes by without stopping, with the people in line for the bus chasing it; also, Lisa is shown riding her bike more (and her sax is in what appears to be a banjo case).
the sopranos made a small change. After 2001 they took out a picture of the 1st world trade center towers.
We’ve been watching Quantum Leap on DVD. The title theme was changed for the 5th season, and I hate it. It’s a new arrangement of the same tune, as if they decided to make it more exciting. But the whole series just went downhill that last season. We’re watching it anyway, but I’m not thrilled about it.
We are reminded of the episode of Monk in which new themes for shows are panned, and it was declared that changing the theme is the death knell for shows.
“F Troop” first season had a theme song with singers and clips from the show and old Warner Brothers movies showing action and characters.
Second season had an instrumental of the theme song and a cartoon mural of cast members and various hijinks on the show.
The opening for Bojack Horseman changes subtly several times during each season. The music and Bojack himself remain the same but what’s going on in the background changes depending on what happened before. For example, when he gets into a fugue state for a few months the pan through the house shows it totally empty.