The sword fight between Robert MacGregor and Archibald Cunningham in Rob Roy.
In Three Musketeers ( Michael York version) the fight in an inn, where they swipe food has a special place in my heart.
I came in to suggest the Inigo/ManInBlack duel from The Princess Bride. The one at the end with count Rugen might have more emotional weight, but it can’t match the spectacle and the fun of that first one. 
The scene in “Old Boy” where the protagonist takes on and defeats a whole gang of badasses in a hallway is so outrageous it has to be up there with the greatest fight scenes on film.
Lectroids, not Lectrodes. Geez, some people!
James Bond vs Red Grant in From Russia With Love. I also enjoyed the sword duel between James Bond and Gustav Graves in Die Another Day.
John Cusack vs Benny the Jet Urquidez in Grosse Point Blank.
Any or all of the fight scenes in Raiders Of The Lost Ark.
Christian Bale’s “gun-kata” scenes in Equilibrium are amazing.
Apparently I posted in the wrong copy of this thread, but I’ll echo that answer here - Happy Gilmore vs. Bob Barker.
Indiana Jones fighting the big Nazi by the plane in Raiders of the Lost Ark.
Clint Eastwood’s Philo Beddoe bare-knuckle fighting with Jack Wilson all through Jackson Hole, Wyoming in Any Which Way You Can.
The Johnny Cage vs. Scorpion fight in the **Mortal Kombat ** movie was pretty kick-ass, as was Liu Kang vs. Reptile.
It’s more than that. Putting on the glasses lets you see things as they really are, not as how the aliens want you to see them. So not only can you see all the aliens walking around among the humans, but you can also see that all the magazines and billboards and street signs don’t say what you think they say. Instead they say things like:
“Don’t Question Authority”
“Marry and Reproduce”
“Obey”
“Watch TV”
“Consume”
It’s a really cool and creepy moment.
Here are some stills from the movie.
Two of my favourites have already been mentioned. Another one:
the fight scene in the training room between the characters of Michelle Yeoh and Ziyi Zhang in Crouching Tiger, Hidden Dragon - Michelle Yeoh use a large assortment of weapons (including a damned heavy iron bar), but her kung fu cannot conquer for Ziyi Zhang’s youth and training.
For Raiders of the Lost Ark, it Indy verses the big bald Nazi under the funky plane.
Rocky vs, Apollo Creed in the original Rocky.
Luke vs Darth Vader (both of them)
duplicate thread, try over here:
I liked the fight between Jason Bourne and the hitman in the apartment in “The Bourne Identity.”
I liked the mention earlier in the thread of Honor Harrington and Nimitz in The Honor of the Queen.
But although some might consider it comical, my favorite filmed fight scene is the bar fight in ST-TOS, “The Trouble With Tribbles” Classic bar fight, with chairs being swung, bottles getting broken, bodies flying, and a guy filching drinks.
*“Laddy, don’t you thing you’d better…rephrase that?”
"You’re right, I should. I didn’t mean to say the Enterprise should be hauling garbage, I meant it should be hauled away* as garbage!"
Scotty carefully puts down his drink, rises to his feet, slugs the Klingon, and away we go!
+1 each for the scenes from “True Romance” and “Rob Roy” mentioned above and adding the fight in the bombed out building between the GI and the German soldier as the cowardly guy watches in “Saving Private Ryan”.
Hugh Grant and Colin Firth in Bridget Jones’ Diary.
It’s one of the only movie fights I’ve seen that actually looks like it could have been a real fight.
shut up
Mr. & Mrs. Smith. Probably the best male/female fight scene outside of…
The War of the Roses