I think my favorite was, is and always will be Eddie Albert and Eva Gabor singing the theme to Green Acres.
All In The Family theme song.
First version, or second?
Are we counting only those actually sung on the show?
The theme for Hogan’s Heroes was sung by Robert Clary, Ivan Dixon, Richard Dawson, and Larry Hovis for this album:
Someone just gave me a bottle of Tullamore Dew to take to Worldcon in a week and a half, so to celebrate I’ll allow off-shoots like yours. 
This one was, of course, done later and much better by Papa Ben himself (but not, so far as I know, on the show):
https://www.youtube.com/watch?v=KLXngS0X8T4Bonanza, of course. Sung by the main cast… now, as I recall, they did this as they rode into the fake sunset in the last episode. But the YouTube clips say it was from the pilot and NEVER NEVER shown on television.
If not, how did I see it ca. 1980… on TV?
oh, on television, you mean?
I was going to ask if “Let the Sun Shine in” counts as the “theme song” to the musical “HAIR”.
Season 2 of Galahad.
I submit this one, just because he’s Chuck Freakin’ Norris! 
The last verse is my favorite! :o
You mean the second version where they sang “Gee our old LA…SALLE…RAN…GREAT” and *still *nobody could understand it?
Before I read the whole sentence I thought you were going to ask about Pebbles and Bam Bam’s “big hit song” on the Flintstones.
Not exactly following the OP’s rules, but Ted “Lurch” Cassidy sang the “neat” “sweet” and “petite” parts in the Addams Family theme, which is arguably the best theme song ever.
I’ve always had a soft spot for this one too, sung by the $6 Million Man himself:
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First version, or second?.
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Honestly, I didn’t know there was more than one version. I’m thinking of the one where they’re sitting at the piano in the opening credits, Edith’s is playing away, Archie’s smoking a cigar, and they sort of lean into each other, proud of themselves, at the end. I haven’t seen it lately, and can’t link to it from work.
The Doris Day Show used a recording of Doris Day herself singing “Que Sera Sera” as its theme song. That seems like cheating because DD was famous for singing QSS more than a decade before the sitcom aired. Her rendition peaked at #2 on the charts in 1956. The 1956 version is a lot better than the 1968 TV-ized version.
The British kids show Here Come The Double Deckers from the seventies. Brinsley Ford went on to sing with Aswad, and Colin Firth had a good career as an actor.
Another vote for the Green Acres theme.