Thanks a lot for the responses. I've actually seen some of the ones you guys listed, but there are a bunch more that I haven't. To give a more accurate depiction of my taste, and what I've liked so far:
Hero - like the multiple stories, but a wee bit too artsy
Once Upon a Time in China - love all of Jet Li's action flicks I've seen
Hard Boiled - sold me on Chow Yun Fat
Drunken Master 2 - I used to own until somebody permanently borrowed it
Princess Mononoke - really liked it, but haven't seen any other Miyazaki films
I've been meaning to see 2046, Ichi the Killer, Audition, and Gozu, but haven't gone through the trouble of locating them yet. I'll make it a priority, though. Thanks again for the help!!