Crouching Tiger, Hidden Dragon is one of my all-time favorites, and one of my most-watched movies.

I like Hero less so...way too much "One China" under "Our Wise Ruler(s)" propaganda for me, though the concept was still really fun. House of Flying Daggers had some cool moments, but otherwise was boring and predictable IMO.

As for other genres,

the Japanese Shall We Dance, that came out way before the joke that was J-Lo's one is one of my favorites.

Eat Drink, Man Woman was enjoyable.

And of course Kurosawa's Seven Samurai is a masterpiece (unfortunately haven't seen any of his other stuff).