It was actually more of a recap of the key events of the *current *season, as viewed from the future. Not “this is what happened in previous seasons”, but rather “this is what’s going to happen this season”.
Subtler than most, but Game of Thrones alters the opening slightly for every episode, apparently to reflect which of the locations in Westeros will be featured in that particular episode.
ER went from a full 2-3 minute opening credits with music to just a quick three second sting somewhere around Season 13 (out of 15). Guess they figured we knew who everyone was by then or they wanted a couple more slots to sell ads. 
Only for one episode. The rest of the season there is a different song over the S2 credits that pertains to something in the episode (and yes, Perfect Strangers was a big plot point in one of the episodes of Season 3).
Isn’t there one wherein the son is giving her a foot massage?
Psych would often do a one-off custom opening reflecting the content of the individual episode. Here is a compilation with just the audio, not the video. (There are others that seem like they may have the video, but they are blocked from viewing in the US.) *Scrubs *also tweaked the credits every year.
And to great effect. For two seasons, we’d start watching every episode with a reminder that the Babylon Project was our last, best hope for peace. Only to start season 3, and to be told right off that <ominous music>
It failed.
“The Good Fight” has one of the best title sequences around. It was tweaked for season 2.
Dammit. I just did a whole thing on Facts of Life with all the links, but hit the wrong key combo on my keyboard and quit Chrome by accident. Grrr. Anyhow, I’ll summarize, all the Facts of Life seasons had at least slightly different intros. The main one:
Original Season One opening. The song is not quite the song we recognize as the Facts of Life theme. This one starts “there’s a place you gotta go for learnin’ all you oughta know about the Facts of Life.” There were actually two more openings that season that slightly differed from each other, so we have three different openings in season 1.
Season 2 has the “You take the good, you take the bad” opening theme song we’re familiar with.
Seasons 3 and four have the same house backdrop as season 2, but slightly different video footage afterwards.
Season 5 introduces Edna’s Edibles as the backdrop.
Season 6 and the first couple episodes of 7 continue this, with some video variations.
Season 7 introduces a screaming electric guitar riff to the intro for who-knows-what-reason and in episode 3 the backdrop changes to the interior of Mrs. Garrett’s new shop, Over Our Heads.
I also meant to write that I remember this being pretty commonplace. Gilligan’s Island is another one. I mean, not only was Season 1 black and white and 2 and 3 in color, but the footage is different and the song is a different recording of the theme. Seasons 2 and 3 also slightly differ, but it’s not a “massive” change as requested by the OP (note the positions of “the Professor and Mary Anne” in the credits.)
ETA: Oh, and there was also the pilot’s intro, which wasn’t aired, AFAIK, but with a completely different, Caribbean-inspired theme song.
Which change happened because Bob Denver didn’t think it fair that two out of seven actors should be listed as just “and the rest”. Apparently his contract gave him the right to say where in the credits his name would appear, since he was the star, and so he told the studio that they could either include the Professor and Mary Anne, or remove his name from the credits entirely.
The final season credits were quick snippets from the previous four seasons, though given how quickly each one went by it was more a reminder for people who already knew the story than a recap that would be any use to viewers coming in late.
I never noticed that! I just enjoyed watching a compilation of them. Did it change with every season or did they rotate them?
One I remember noticing as a kid is That Girl. I only saw it in reruns, of course, and I was always disappointed if there was no singing. Not only did I like signing along, but it was the later seasons that had lyrics and I like those episodes better.
In the early seasons, she’s soaking her feet at the end of the opening credits, but that’s about it, IIRC.
There’s a third version where he does a slow step around the ottoman, then trip on the carpet.
The Christmas episode ends with the cast “singing” the theme song, complete with a sound effect of him tripping over the ottoman, but in the opening, he sidesteps it.
The show changed its title as well each time (Aqua Unit Patrol Squad One; Aqua Something You Know Whatever; Aqua TV Show Show; Aqua Teen Hunger Force Forever), much to the dismay of those of us with DVRs that would miss the season premieres because they were under the previous title.
Well, except the last season, which used the “Mother Hale” opening that they started using during the previous season until Cosby pulled it (and brought back the previous season’s “Apollo Theater” opening) over a disagreement about what compensation should be paid to the creators of the original Mother Hale mural).
Another one: Eight is Enough changed its theme song from an instrumental with the family making a human pyramid to one with lyrics and having scenes from previous episodes.
As for why shows would do this, one possibility is, opening credits are an Emmy category, but after a show’s first season, the show requires that the credits be “substantially changed.”
Nope, the last two seasons (the last year and half of which almost no one saw because ABC tried cancelling it early, but drew was all, oh hell naw, contract, beeotches! and kept making them so ABC buried them in the summer doldrums and aired them massively out of order) used covers of all three themes over various different scenes.
They also had to change it for cast changes, like adding/removing George Clooney, replacing Charlotte Rae with Chloris Leachman, and adding Mckenzie Astin and that australian girl (the character was Pippa, dunno the actress’s name). And they removed the store entirely near the end to build bedrooms for the new kids.
It’s original parent show, Diffrent Strokes also had massive intro changes in the last season, including a “diffrent” mix of the theme song and new shots of the appartment (apparently all changed on the set when it moved from NBC to ABC)
It was aired, decades later, on Nick at Nite.
Blackadder was radically different each season.
The Wire had the same song (Way Down in the Hole), with different artists/styles each season.