Gilligan’s Island - Not only do the lyrics change from “and the rest” to “The Professor and Mary Ann,” it seems that there are new vocalists singing the song. The later voices are deeper.
The Brady Bunch - More mature voices in the later seasons. Did the actual kids sing either version of the theme song?
Happy Days - Changed from Rock Around The Clock Tonight to a generic, show-specific song, for reasons that elude me.
Mike & Molly - First few seasons the theme was slow and bluesy. Now it’s the same words and same performer, but much more up-tempo. And I hate it.
The Drew Carrey Show - the first season had a short jazzy bit, then they changed to this 1960s pastiche, and then, in the third season I think, they settled on the Presidents of the United States of America and stuck with them to the end.
The Wire used a different version of the same song for each season, didn’t it? I remember one of them was really good, but don’t know which season. I gave up on it somewhere in the middle.
This was deemed too depressing by the Scifi channel, so they had Bear Mccreary make a new one without the singing. I don’t have a link to it, but it was nice too. However, it was even more somber sounding(intentionally so, I believe).
So in the second season, the US switched to the vocal as well.
Oh yeah. Simon & Simon had two different songs, too.
Semi-related to the topic: I was in Brazil in the 80’s and they mixed up all the theme songs for the American TV shows. I seem to recall Hill Street Blues with the theme to Magnum P.I., Magnum had the later version from Simon & Simon, and that show used the early version, with English lyrics.
Dirty Jobs originally had Faith No More’s “We Care A Lot” as the theme song. Then it went to a generic tune that sounded similar because they didn’t have the rights. Then it went back and forth a few more times. It seems like a crapshoot when you watch the older epsidoes as to what you’re going to get.
The pilot for Lost in Space borrowed the theme song from The Day the Earth Stood Still; subsequent episodes used the more commonly-known theme song written by Johnny Williams (yes, aka John Williams).
The Cosby Show incorporated true variations of a theme with each season featuring a different version of the basic melodic structure of their opening song.
This was actually a request, or demand, from Bob Denver (Gilligan) that the remaining cast members, The Professor and Mary Ann be added to the theme song. The studio balked at the cost of redoing the song but that crazy Gilligan prevailed.
Weeds had a song during the first season and kept that song in the second, although it was different every episode, because it was sung by a different artist.
Sometimes it was sung by country singers, sometimes by opera singers, sometimes by rappers…
Doctor Who has had numerous arrangements of the theme over the last 50 years.
Star Trek season 1 - instrumental theme
Star Trek season 2 - added ahhh-ahhh-ahhhs