This happens to a lot of movies. A decent, entertaining film gets a bad, bad trailer that makes it look not-so-decent and fairly stupid. It happened with The Iron Giant and now it has happened to Shanghai Noon.
Jackie Chan plays Chan Wang, an imperial guard who goes to the American old west to rescue a kidnapped princess (the incredibly hot Lucy Liu). On his way, he teams up with bumbling outlaw Roy O'Bannon (Owen Wilson), a sort-of cowboy/surfer hybrid. On their way, they battle Roy's former gang of idiots, a corrupt marshall, and a former Chinese imperial guard who now enslaves Chinese immigrants to work on the railroad.
First off, Owen Wilson gives one of the funniest performances I have ever seen. His whole low-key, self-referential approach to being a cowboy had me in stitches, and is the perfect foil for Jackie Chan's wound-up high energy persona. The writing is clever and the dialogue quotable. Perhaps the story is a bit predictable, and gets a little too serious whenever the princess plot is addressed, but it doesn't matter. The ride itself is well-worth it. The fight scenes are fast, funny, and entertaining, unlike, say, Mission: Impossible 2's.
I've seen it three times, believe it or not, and I recommend it to anyone looking for something fun and light-hearted and just plain good to see.