Hand to Hand
Drunken Master 2 - Jackie Chan and some dude. I don't remember the story, but I remember that I saw the most amazing display of martial arts in cinema history.
Sword Fight
Crouching Tiger Hidden Dragon - the one between Michelle Yeoh and Zhang Zhiyi at Yeoh's place, near the end.
Comedy
Bridget Jone's Diary - the one between Hugh Grant and Colin Firth. The most pathetic fight in history.
Gun/Shooting
Landing at the beach scene of Saving Private Ryan.
Medieval Battle
The Battle of Helms Deep - THE TWO TOWERS
The Fight that made me cry
Luke chopping off Darth Vader's hand in Return of the Jedi.