Crouching Tiger, Hidden Dragon (2000)

Directed by Ang Lee, this movie is based on a wuxia novel written in the 1940's. Though the movie was overall well-received by western audiences, the fight choreography by the seemingly ubiquitous Yuen Woo-ping was fairly bland, with the exception of this duel between Jen (Zhang Ziyi) and Yu Shu-lien (Michelle Yeoh).

I enjoyed the ferocity of the fighting as well as the variety of weapons employed by Yu Shu-lien against the seemingly indestructible Green Destiny sword.

Star Trek TOS: Episode 18 - Arena (1967)

Quite possibly the worst fight scene ever choreographed, this duel between Captain Kirk and the Gorn captain is so bad it's good! Despite (or perhaps because of) the crude, almost laughable, action in this episode, the slow-moving but tough Gorn captain has become one of Star Trek's most popular aliens.

The lizard suit was designed by Wah Chang, who also created such memorable Star Trek props as the tricorder, the communicator (which is thought to have inspired modern "flip" phones), and tribbles.