Uhura sings “Beyond Antares”(sp?), which sort of sounds like the “Star Trek” theme, but whether she actually sang words to the theme, I don’t know.
Try singing this to the theme of “Superman” movie:
Look up in the sky,
Is it bird?
Is it a plane?
It’s SUPERMAN!
Hah!
I prefer the version from the movie, “Dave”, from Dave singing in the shower, “Hail to the Chief he’s the one we all say ‘Hail’ to…” 
I read that in TV Guide, and it’s exactly what I sing when the show comes on.
I also sing to Bewitched: “Bewitched, Bewitched, the theme song from Bewitched (x2) …”
Then ad-lib something, usually about how Darren #1 is better than Darren #2, and at the final flourish, “On Nick … At … Night!”
This may be why I am still single.