Im not saying these are the "coolest" neccesarily, but they are some cool ones off the top of my head. Lethal weapon Fast 5 Gangster squad The incredible hulk Jack reacher Expendables 2
Indiana Jones and the Sword Guy Doc Holiday and Johnny Ringo Jason Bourne in pretty much any fight sequence
Probably not because of one on one fights but because I like the film generally I have to say John Wick is amazing.
Michelle Yeoh and Zhang Ziyi "Crouching Tiger, Hidden Dragon." The kind of girl on girl action that even NoFappers can enjoy!
If you're into more realistic swordfights in movies: Princess Bride: Rob Roy: Kmicic vs. Wołodyjowski - I love it, as it shows a brawler who thought he was the best in the country fighting with a short man, and actually the best swordsman in the country. Kmicic's technique becomes more and more chaotic, as he realises how strong his opponent is. At 4:25 Kmicic finally understands and says 'Finish, spare the shame', to which Wołodyjowski agrees...
I absolutely love the princess bride and that sword fight seen is classic. Ive never seen the other ones though.
Yes, animations! As I mentioned, I'm into realistic representations (or those that are pretty close to real-life techniques), and I must recommend this one: The Boy and the Beast (sadly, I can't find the part with their sword duel): Some Naruto (less realistic) hand-to-hand combat scenes are also great. Plus most Cowboy Bebop fight scenes. Spike is really good!
Anakin v Obi Wan (in the Revenge of the Sith) More of a hunt than a fight, but Richard Benjamin v Yul Brynner in Westworld Ali v Liston in Ali
I love the light saber duels, but they just go on for too darn long! The Bourne movies were good fight scenes, but to film it, it looked like they duct taped a video camera to a squirrel running around in the same room. I just want to scream, "HOLD THE FRIGGIN' CAMERA STILL!!!!!" I love the scenes with Liam Neeson in the Taken movies - short but awesome! And just about any Michael Jai White fight scene, but especially this one: (There is some bad language)
Ha ha, you are right about the bourne movies, they are sweet, but the squirrel thing is a perfect description.