I’ve always been partial to the theme for “Alfred Hitchcock Presents”
Gounod’s
Funeral March of a Marionette
Night Court
Barney Miller
Newhart
St. Elsewhere
Family Guy
Knight Rider, by far.
Or the final 1:27 of Fleetwood Mac’s The Chain, which was the theme song for Formula One racing when it was on the BBC.
Play it for almost any British person and they’ll think of motorsport.
If we’re going to include lifted pieces on factual programmes, then that is beaten by Whole Lotta Love being used as the Top of the Pops theme for many years. It was so popular that when they changed it, there was so much fan outcry that they had to change it back.
Definitely the Doctor Who theme: moody, scary electronic instumental music conjured up by the BBC Radiophonic Workshop before synthesisers had even been invented {and has been hugely covered}.
Batman, just because it’s such fun {and has also been hugely covered}.
And The Simpsons theme, by Danny Elfman: a subtle yet perfect Leonard Bernstein homage {especially the numerous closing credit variations: Hill St Blues, Sonic Youth, Addams Family, Phillip Glass…}
I agree… I used to watch Hamtaro specifically so I could hear the beginning and end theme songs… in the same vein, though not English, but anime, I love all the goofy, poppy, sugary sweet music from CardCaptor Sakura… :o Oh, oh, and Ryu Kumon’s theme from Ranma 1/2… “Battle Renaissance” - woo!
Anyway… back to North America… 
I actually really enjoy the theme for Desperate Housewives.
As a child I loved the Nightcourt theme.
Here’s another vote for Futurama.
**The Simpsons ** is classic.
Pink Panther
The Monchichis
And… hee… **The Fresh Prince of Bel Air ** always makes me and hubby groove.
The Avengers
Twelve O’Clock High
UFO
Captain Scarlet
The Baron
Where’s the love for Dave Grusin’s excellent effort for It Takes a Thief? Well, maybe part of the charm was the period footage used in the opening credits to convey hipness - the skiers spraying snow, the spinning roulette wheel, you know.
“Let me get this straight - you want me to steal?”
More votes for Dr Who and Knight Rider
I’ll also throw The A-Team into the mix
Battle of the Planets was also a long-time fav. 
Perfect Strangers is without question the greatest.
The Name of the Game was a forgettable show with a great theme song. Dave Gruisin wrote it, along with the themes to The Bold Ones, Dan August, The Ghost and Mrs. Muir, Good Times, It Takes a Thief, Maude and St. Elsewhere.
See here for a list of Druisin compositions.