Some great Chinese movies (non-martial arts) that might be of interest:

mainland China:
World (Jia Zhang-ke)
Platform (Jia Zhang-ke)
Unknown Pleasures (Jia Zhang-ke)
Raise the Red Lantern (Zhang Yimou)
Story of Qiu Ju (Zhang Yimou)
Red Sorghum (Zhang Yimou)
Yellow Earth (Chen Kaige)
Farewell My Concubine (Chen Kaige)
Blue Kite (Tian Zhuangzhuang)

Taiwan:
Yi Yi (Edward Yang)
Flowers of Shanghai (Hou Hsiao-hsien)
Millenium Mambo (Hou Hsiao-hsien)
Goodbye South Goodbye (Hou Hsiao-hsien)
Good Men Good Women (Hou Hsiao-hsien)
Time To Live Time To Die (Hou Hsiao-hsien)
Wedding Banquet (Ang Lee)

Hong Kong:
In the Mood For Love (Wong Kar-wai)
Chungking Express (Wong Kar-wai)
Happy Together (Wong Kar-wai)
Fallen Angels (Wong Kar-wai)
Days of Being Wild (Wong Kar-wai)
2046 (Wong Kar-wai)
Actress (Stanley Kwan)
Rouge (Stanley Kwan)