Off th’ top o’ my head…
Paul Newman’s fight with the Stasi officer in Torn Curtain.
Godzilla vs. the Super-X in Godzilla 1985.
The Samus/Master Chief fight in Haloid.
(Really more because of the spectacular scenery, but…) The first thing that comes to mind is the opening of Silverado.
Family Guy, Peter Vs Chicken
Highlander, the original movie. The scene where Mcleoed turns up to a duel drunk, Gets stabbed, falls down, gets up, staggers towards his opponent, gets stabbed, falls down, gets up, repeat.
Fight Club, Tyler vs “narrator.”
How about Robert Carslyle as Begbie against anybody in Trainspotting.
And, Bugs Bunny vs. Daffy Duck vs. Elmer Fudd in Rabbit Fire.
Edward Norton v. Edward Norton in Fight Club .
Blade versus Frost as La Magra.
Benedict versus Corwin in the Amber series; Guns of Avalon IIRC.
Agreed. The scene before (against the Crazy 88) is also great.
The Lighthouse scene, in Battle Royale.
You cannot go wrong with what Tony Jaa does. He has so much talent. Here is an example from Ong Bak
That’s the one I came here to mention. One long tracking shot, just ridiculously great.
Me too.
The Operatic Kung Fu Fight from The Fifth Element.
The bar fight in Dirty Work. And then the next scene. Comic genius!
If we’re doing literary fight scenes, then my favorite has to be the duel between Lord Oberyn Martell, the Red Viper of Dorne and Gregor Clegane the Mountain that Rides from George R.R. Martin’s A Storm of Swords.
“Elia of Dorne. You killed her. You raped her. You killed her children. SAY HER NAME!”
That’s a great scene. 
I would add several more from that movie e.g. when a policeman and two helpers try to arrest Jade Fox…
I’m a monkeygirl, what can I say. 
You’ve all missed the big one: the pie fight from Blake Edwards’ The Great Race. 
I know The Great Race has been mentioned twice now, but I would put forth the barroom brawl (with Larry Storch as the instigator) in that same film as the best of that type of fight.
Since there were two threads, I’m merging them. (That causes a little hiccup in the fabric of the space-time continuum, but just ignore that and go as you were.)
Has anybody mentioned Frank Sinatra and Henry Silva in The Manchurian Candidate? I think it was the first karate fight in a mainstream American picture. Nothing fancy, just direct, brutal confrontation. (Sinatra wasn’t a big guy, but I wouldn’t have messed with him.)
Nope, let me correct myself. Seven years earlier, in Bad Day at Black Rock, Spencer Tracy kicks Ernest Borgnine’s ass as a one-armed veteran who uses karate to make up the difference.
As an SCA guy, I’ve got a special fondness for sword fights, especially with a medievalish setting. I really enjoyed Aragorn vs. the Uruk-hai leader in Fellowship of the Ring, but my sentimental favorite would have to be Charlton Heston in El Cid, as the King’s Champion, fighting for ownership of a city; can’t remember who the other actor was, but they looked like they were seriously trying to kill each other.
Even though it’s an absurdist comedy, Monty Python and the Holy Grail actually has a really good fight scene: the Black Knight’s first fight (before the one where he unfortunately loses all four limbs). John Cleese and (if I recall) Terry Gilliam did that themselves, without formal training, and showed real enthusiasm.
The last battle between Optimus Prime and Megatron, in Transformers: the Movie.