I was going to open a thread up on this guy's death, so well done sysyphus.
Robert Moog is/was a bedrock for modern music, all electronic music. The Moog has been used in all kinds of genres. One very famous example which people have mentioned, especially for Trooper, is "The William Tell Overture" in a moog style, which was used by Kubrick in Clockwork Orange. FYI - It's used in the scene where Alex meets two girls at a record shop and takes them back to his place for some double speed rumpy pumpy to this music.
The Moog has also been embraced in a big way by the jazz world. The Moog, along with the Hammond B3 and certain Yamaha models have been instrumental in Jazz's rejuvenation in the face of rock music's rising popularity in the 60s and 70s. Originating in gospel churches these 'electro keyboards', including the Moog, refreshed gospel music and in turn refreshed many a Jazz, Soul, R'n'B, Blues, Funk etc musician. Just a few names who will surely be tipping their hat to Robert Moog:
Ray Charles (used a Yamaha based on Moog principles)
Herbie Hancock (keyboard maestro who fell in love with all these electro keyboards)
Miles Davis (the godfather of jazz fusion music, which depended on electro)
Marc Moulin (a very rare and seriously influential Belgian jazz musician)
Piero Umiliani (another rare one - he wrote "Ma Nah Ma Nah" which was originally for an Italian porn film but was made famous by The Muppet Show)
Jimmy McGriff, Shirley Scott and Jimmy Smith (all made the Hammond B3 sing like a wonder)
Another interesting off shoot of the arrival of the Moog was the idea of holding Synaesthetic Concerts, ie. concerts which entertained a number of senses - especially hearing and sight. This was happening in the 50s and 60s and instruments like the Moog were being hooked up to all manner of optical projections to provide light shows that ran simultaneously with the music. This sadly died out for some reasons which I can't quite remember.
The Moog is also the instrument behind many a sci-fi B-Movie soundtrack. An instrument related to its usage was the weird and wonderful Theremin, which was also used in the multi sensory concerts mentioned above.