I know Game of Thrones got a ton of hate after a while, but I loved the intros. They were unique to the setting where the episodes were going to take place.
The worst intros are the long ones that never change, but are on every episode.
They evolved to show the status of the elements on the map as events unfolded, it was honestly a really good subtle recap of major happenings up to that point in the story
The series went to shit, but the intros got me hooked from the very beginning (like, holy hell, what is this?) and I never skipped a single one, even at the end when I was pretty much done with it all.
Also, remember the single episode that just started with the Hound? That was a trip, when you expect the music and map.
Gotta say: The Simpsons. Danny Elfman made one of the most iconic intro songs, and while I'm not sure the Simpsons was the first to do it, the varying intros was another iconic element.
I really like the intro for Disenchantment as well.
Song of the Bandits The song on the YT video isn't great here imo, but they actually mix it up in the show proper and use different songs. And some really fit the theme.
If we're talking about music in general through the show rather than just the intro - The Korean High Fantasy series Arthdal Chronicles. Some stunning, music, throughout, the show. It was also kinda like watching a JRPG (even if Korean).
I'll always enjoy the intro to stargate atlantis just because the whole concept of the city (and it's appearance) is so fucking cool, even with the noticably.. Sufficient.. CGI it's so inherently neat that it'll remain impressive.
Weeds. I believe starting in S2, they start doing the same song, same intro, but in different styles. I believe they even had green day cover it at one point.