well if by chinese you mean mainland not hong kong, check out anything by Zhang Yimo. action (hero, curse of the golden flower, house of flying daggers) and drama (to live, rise the red lantern, not one less) that's from the top of my head. he has lots more. most of his films are really good.

I love Feng Xiao Gang‘s movies！

Great humor!

And for Hongkong, I love Wang Jia Wei.

The Forbidden Legend: Sex and Chopsticks (金瓶梅) 1 and 2... Anything Stephen Chow Sing-Chi (周星驰)... Farewell My Concubine (霸王别姬)... To Live (活着)... The Blue Kite (蓝风筝)... Ju Dou ( 菊豆)... Raise the Red Lantern (大红灯笼高高挂)...

Red Cliff 1 & 2 are good action movies, directed by John Woo, and they must be one of the best parts of The Three Kingdoms story.

For drama, "Aftershock" the movie about the Tangshan earthquake is very well made

if you like romantic genre, try The Love of the Hawthorn Tree and You.Deserve.To.Be.Single. These movies were released in 2010.
If you like acton, He Man: the sequel to The.Underdog.Knight is released few months ago
if you like Jackie Chan, 1911 ( this movie will release in Dec 2011, I think)

I'm with Rich45 on this one - Hero is excellent.

i recommend you to see "crazy stone" and " let bullet fly " movies that are very instersting. if you want see kung fu movies, don't see those films produced by mainland directors. most of them are trash. Hong Kong action movies still better than mandarin.

Red Cliff was great and historical which made it all the more itneresting though most movies in china are somehow based in history for some reason. they don't usually come out with whimsical ideas that are complete fancy. I don't know the names of any of the chiense zombie movies i saw but they are ridiculous and worth a look up.

Deadly Delicious, actually a very stylish Chinese thriller
http://www.imdb.com/title/tt1000775
might be hard to find...

Start with the entire Jackie Chan back-catalogue.

Then move on to Zhang Yimou's works (entire catalogue).

Then Chen Kaige.

Then Wong Kar-Wai (Hong Kong).

Finally, watch some later Donnie Yen stuff.

And to round it all off, check out everything Sammo Hung has done.

Congratulations. You are now an expert in martial arts and Chinese film. Have a red star.

Also: The Horse Thief, Yellow Earth, Suzhou River.

Anything you can find by: Jia Zhangke, Lou Ye, Li Yang, He Jianjun, Zhang Yuan, and others.

Sometimes difficult to find the movies with English subs, and also the best directors of China have been blacklisted at one time or another, as well as some of the best movies to come out of China.

I agree with all people here. Raise of the red lantern is really good!

  'A World Without Thieves' with Andy Lau is an excellent movie. Good subtitles too.

Lust Caution. Awesome!! and has the sexiest Chinese actress ever!!

BBC : Ai Weiwei, Without fear or favor.

http://www.youtube.com/watch?v=gcRodOfu_s8

Not Chinese, but about a Chinese...what a man!

Theres a new documentary about him too, can't find it...

http://www.imdb.com/title/tt1845773

http://en.wikipedia.org/wiki/Cinema_of_China

Farewell my Concubine  霸王别姬

Chungking Express 重庆森林   (a hong kong film but one of my all time favorites, there's a lot more to it than just the plot, i strongly recommend it.)

Crazy Stone is also pretty good, not sure if theres English subtitles for it 疯狂的石头

I watched Let the bullets fly (让子弹飞) last year. I wouldn't say it's a must-see, but it was a pretty nice movie.

life without principle