Sometimes, a TV show changes its distinctive theme music. Sometimes it’s a subtle variation on the original, that makes total sense. Sometimes it’s a clean break from Season One (Lost in Space, Monk). Have you ever preferred the new one?
I think Everybody Loves Raymond had multiple theme songs. My preference is Jungle Love, just because I like the song.
I was pleased when they added “the Professor and Mary Ann”. Especially Mary Ann, as I firmly a camp Mary Ann type of guy! 
I liked how “The Wire” had different versions of Tom Waits’ “Way Down In The Hole” for each season.
The Cosby Show had a different theme song each season. I had no particular preference, though.
Monk changed it after the first season. I preferred the new one because I like Randy Newman.
The Drew Carey Show had a variety of theme songs, each with a song and dance routine by the cast. Cleveland Rocks was the most often used, but I really liked What is Hip? Five O’Clock World was the original, I think, and probably my least favorite.
Probably cheating as they are basically the same song, but I liked Tennant’s version of the Dr. Who theme the best.
That would be “Moon Over Parma.”
I thought Peep Show made the right choice when it switched to Harvey Danger’s “Flagpole Sitta” from whatever that knockoff “Curb Your Enthusiasm” theme was.
I much preferred the use of “Rock Around the Clock” for the first two seasons of Happy Days. Garry Marshal must have gotten sick of writing royalty checks to Bill Haley.
Original Monk fan here.
Marci Maven: "if you ever get your own tv show never change the theme song”
Hawaii 5-0s iconic (it should be the national anthem) theme music actually changed nearly every year. Just the arrangement, not the tune itself. But, to the OP, I’m not sure which one is best.
I think it would be a lot better than the current “To Anacreon in Heaven” tune.
The song and opening credits scene of the second season of Peacemaker grew on me but I still prefer the first season.
I prefer 3rd season Lost in Space theme but I’m a sucker for French horns.