The other day I had “Come and knock on my door, I’ll be waiting for you.. where the kisses are hers and hers and his, Three’s company too” stuck in my head.
There are so many others that can easily be remembered.. Gilligan’s Island, Brady Bunch, Cosby Show (they had a few), Family Ties, Facts of Life, etc..
It’s funny after all these years that I can remember those songs, but can’t remember important facts for my exams. If only they could test you on this vital information 
"Wings of my dreams"
this was the theme for Perfect Strangers, if I recall!
Perfect Strangers used to be my favorite sitcom, alongwith 'Mind your language' which was a British sitcom about a classroom with adult students from different counteries.
I never paid attention to their theme songs though. The only two theme songs I remeber now are those of 'Cheers' and 'Friends'.
And Nusaiybah, you are right, they never ask you what's more important in exams. I remeber when I used to have exams back home and at the same time Indian or English cricket team would be visiting Pakistan for series... I would always know the latest score etc. and they never bothered to ask me that in exam... It always used to be stupid chemical formulae or element symbols or those non-sense Laws of Newton. You tell me, what's more important? Zaheer Abaas' century or E = MC^2?
I used to love Perfect Strangers too. "Cousin Larry, Don't be Ridiculous" (Of course in the Balki Bartakomous accent). He used to have some of the best lines.
I don't know that other program, Mind Your Language, but I do have a British fave.. Mr. Bean! He's hilarious!!