Some of my favorite theme songs include Cheers, WKRP in Cincinnati, Little House on the Prairie, The Patty Duke Show, Newhart, and the original opening to Walt Disney's show when it was called Disneyland and was in b&w.
Surprised to see that F Troop has only been mentioned twice. The black & white season 1 opening is one of the best in my opinion.
And while I love all of the Dick Van Dyke Show, my favorite is the very first opening with the pictures. They cut that down later in season 1 to shorten it and then...
Little House on the Prairie is my favorite. For about 10 years, the intro theme has been the startup tune on my PC and the end credits play when I shut it down. :)