They used the *Brisco * music for the last Olympics too.
I’m a huge Bruce and Brisco County fan too. As of now, the show is NOT on DVD, but it seems almost inevitable that it’ll get released eventually. I’ll be first in line when it does! I remember it being a terrific western-comedy, with bizarre sci-fi touches (almost like a “good” version of the horrible Wild Wild West movie).
I’m sure I’ve heard this one too (assuming I’m thinking of the right one).
Too soon forgotten: Chuck Mangione wrote the theme (c. 1980) for the Winter Olympics at Lake Placid, entitled “Give It All You Got.” Not the best grammar, but that’s the way people talk, sooo . . . Oh. It also won an Emmy. 
Get out of my head!! I’ve been singing the same thing!!
(Do you also sing “It’s a bird, It’s a plane, It’s a Moz-art!” for the Jupiter Symphony?)
For me, THE Olympic theme is Bugler’s Dream by Leo Arnaud. That’s the piece with the kettledrums and chorus of trumpets.
Fun personal fact:
The opening ceremonies for the 1984 Olympics in Los Angeles featured a 1000 voice choir sitting at one end of the L.A. Colloseum, made up of university choristers. I got to be one of them.
Unfortunately, the voices you heard singing on TV during said Opening Ceremonies were not those of the live choir, they were pre-recorded about 2-3 months earlier and consisted of about 70 handpicked members of that 1000 voice choir. I was, sadly, not among the 70 chosen for the recording chorus. (Had I been at UCLA for a couple more years, I think I could’ve made the cut.)
They also used the Jurassic Park music in an episode of Nova about a masterpiece tile mosaic floor that was dug up from an area in Turkey just before a new dam went up and flooded the place.