Family Guy notoriously had a bit in the original theme song that, to some viewers at least, didn’t sound like what was intended. After the chorus sings
“Lucky there’s a man who
Positively can do
All the things that make us…”
Stewie says “Laugh and cry.”
Somehow, viewers took that as Stewie saying “Effing cry.” It was changed in later seasons to have Stewie enunciating the words “laugh and cry” more clearly.
FWIW, I never thought it was anything but “laugh and cry.”
I think all the opening themes were the same - it was the title animations that changed. There were four or five different end-credit themes, all sung by Kelsey Grammer.
(It takes an act of will to spell that word with an e…)
“Petticoat Junction” adjusted the lyrics to match changes to the cast. The original had the line “it is ran by Kate come and be her guest” and the later one had “there’s a lady MD, she’s as pretty as can be”.
John Williams wrote two different themes for the series. The second one (in whjich the opening titles started with a countdown) was better than the original first season one. But the first season theme wasn’t related to Bernard Herrman’s Day the Earth Stood Still music. I haven’t seen the original pilot (no Dr. Smith), so I don’t know what they used there.
Farscape went from having a non-verbal song that sounded like an orgasm, in its first season… to a different non-verbal song that sounded like a completely different orgasm, in later seasons.
They’re completely different because they’re different stanzas of the same song. That certainly constitutes a change in theme song in accordance with the OP, of course. But the refrain was re-done from the uncertain, “you might just,” to the more optimistic, “you’re gonna.” That was a change in the lyrics, not just a different stanza.
Well, the theme music to Baretta never changed, but in the first season, “Keep Your Eye on the Sparrow” was an instrumental. Starting in Season 2, the song had lyrics sung by Sammy Davis Jr. (*And who knew more about the mean, crime-ridden streets than Sammy?)
Like the Star Trek theme, The Munsters theme had lyrics that were never heard on the TV show (or in the movies, IIRC). A vocal version was, however, released on a children’s LP, and I got a copy for Christmas 1965:
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Years later, Butch Patrick released a single, “Whatever Happened to Eddie?” set to the tune of the Munsters theme. His lyrics even contain a nod to those original lyrics, with the line about your hair turning white after peeking through a window screen.
New Girl has changed. The theme song used to be a slower version with a singing part (by Zooey Deschanel), but now its a quicker version of the original without singing.
CBS Sunday Morning has had multiple versions of its baroque trumpet theme music (“Abblassen” by Gottfried Reiche). The most recent version is performed by Wynton Marsalis, who gussied it up with a bunch of fancy fillips and runs & crap.
We recently watched seasons 1-8 in a pretty continuous stretch. The opening credits and theme are very short - maybe 10-12 seconds - and I can’t bring any variations to mind. There were a number of variations on the animation of the “Frasier” logo, however, some seen only once each.
The end-credits song had several variations that rotated, mostly varying in the last few seconds/closing words.
If there are further variations in seasons 9-11, I wouldn’t have any good memory of them.