Not sure that this is the correct forum for this thread, but it's general, and while I'll only cite dramas in this first post, it could easily apply to some sitcoms. IOW, I'm tryin'. :)

In this, please specify both the show and the channel it's on (some other 'nets may have paid for the original music)

Las Vegas on Cozi.
Magnum P.I. on Get TV

I noticed that when the original Charmed aired on SyFy (they for whatever the reasons, only have Seasons 1-3 AKA the Prue/Shannen Doherty years), they don't play (https://www.reddit.com/r/charmed/comments/105sqd6/title_music/) "How Soon is Now?" (https://en.wikipedia.org/wiki/How_Soon_Is_Now%3F) by Love Spit Love during the opening credits (https://charmed.fandom.com/wiki/Charmed_Opening_Credits). Instead, it's some bland, generic, instrumental "sound a like" version.

On Hulu "Designing Women" doesn't feature the correct opening sequence for most seasons post season 2, instead of using the popular black & white photographs opening they use the same opening from season 1 with the picture frames for most of the episodes, except they did keep the Ray Charles opening for the Julia Duffy season.