I would like to mention Bruce Lee's Kid Brandon Lee

In Rapid Fire, Brandon Lee duels "The Henchman" bodyguard played by the great Al Leong.

The fight represents one of the best representations of a real streetfight using JKD and Wing Chun.

...and how bout "Scanners" Psychic duel head explosions!!!

Inigo and Westly's (this came up before, but there is a T in there!) duel is the best for sure, but I think there's something beyond the choreography and the context that makes that fight so perfect - the music.  It's as much a part of that scene as Cary and Mandy.  The music is seemlessly integrated into the fight and practicaly comes to life as another character.  

I'd also put the duel between Westley and Humperdink on my list, too.  "To the pain" is one of the best exchanges of all time.  It's a verbal duel and Westley utterly destroys Humperdink with his words alone.  It remains, to this day, possibly my favorite scene of all time.

How in the hell is Kirk vs. Khan for the thrilling finale of "The Wrath of Khan" be left off this list?!?  Hmm, must be on dope at Mania. 

Wesley vs Montoya is perfect, and so many others mentioned here for sure, but my favorite is Neo vs Smith at the end of the Matrix.  Just had everything you wanted and the most perfect ending in the history of movies in my opinion.  Everthing since has tried to have a little bit of the Matrix in it I think.  I also think the sparring match between Neo and Morpheus was pretty amazing too!  Actors never had that kind of commitment to training and selling it like they did in that film and it changed the way actors prep for roles these days.

Edward Norton vs Edward Norton in his bosses office, and Edward Norton vs Tyler Durden at the end of Fight Club.  That movie might as well be called "Man-movie"