This leaves out a lot of great tunes. I dropped The Bullwinkle Show and Gomer Pyle USMC from the list to put in My Three Sons and Captain Kangaroo. I know the Captain isn't technically a sitcom, but that's a great theme song and it deserves to be on the list.
A lot of these are very memorable and you won't need to click on them to remember them, but I recommend a click on That Girl. The theme by the late Earl Hagen is a beautiful arrangement. I love the pizzicato strings.
For anyone who might ask if it's Dick York or Dick Sargent on the Bewitched link, please. I'm not a philistine.