I first saw this movie with three friends at a theater in Norman, Oklahoma when it first came out. Aside from the four of us, the usher was in the theater, and the projectionist too. They should've gotten combat pay.
The US government goes to a gymnast to get him to train for and participate in The Game, a decathlon cum obstacle course held each year in the tiny country of Parmistan (the four of us immediately decided its major export was Parmesan cheese...). The Khan of Parmistan grants each winner a favor, and the US wants our hero to ask pretty please to let the US put some kind of radar installation in Parmistan to support SDI. Our hero agrees--after all, his dad mysteriously disappeared in Parmistan.
Our hero gets some help from the Khan's daughter, who turns out to be the only citizen of Parmistan who looks even vaguely Asian. (_Gymkata_ was filmed in Zagreb, then in Yugoslavia.) There are people who want to stop him, though--fortunately, every place our hero is in danger, there happens to be a convenient piece of gymnastic equipment that he can leap onto and kick some enemy behind. (It even comes pre-powdered so his hands won't slip--they think of everything!)
A high point of the film is the Khan himself, and his pronouncements from the balcony. We in the theater swore up and down that Mel Brooks was playing the Khan... He always uttered some non-English interjection that we promptly forgot (UPDATE: it's "yakmalla!"), replacing with "Uff- da!" when imitating him during and after the film, and followed it up with "My people!"
I recommend this in a double feature with _Phenomenal and the Mask of Tutankhamen_. Think you need an Abdomenizer? Nope--just watch these two movies.