Auf Wiedersehen Pet, both opening & closing titles in series 1 & 2, one of the few series that had different opening & closing songs, Joe Fagin [the singer, not the Liverpool manager ;] sang the theme.
Brookside, try & guess the location shots in the opening titles.
Blackadder
Ted Lasso, shame it's only the chorus which lasts just over 10 seconds, the full theme [Marcus Mumford, Heaven Knows I Tried] is good
Quite a lot of the US TV shows have great themes too, often extended opening titles.
The Royle Family, Oasis, Half The World Away, even Noel Gallagher has said, he thinks Half The World Away is more The Royle Family theme, than an Oasis song.