Here are my favorite films from China, Hong Kong (now part of China), Taiwan and South Korea (including co-productions).

Rated 10/10
Yi Yi: A One and a Two (Yang, 2000) (Taiwan/Japan)
In the Mood for Love (Wong, 2000) (Hong Kong/China)

Rated 9/10
Spring in a Small Town (Fei, 1948) (China)
Poetry (Lee Chang-dong, 2010) (South Korea)

Rated 8/10
Raise the Red Lantern (Zhang, 1991) (China/Hong Kong/Taiwan)
Farewell My Concubine (Chen Kaige, 1993) (China/Hong Kong)
To Live (Zhang, 1994) (China/Hong Kong)
Eat Drink Man Woman (Ang Lee, 1994) (Taiwan/US)
Xiu Xiu: The Sent-Down Girl (Joan Chen, 1998) (Hong Kong/US/Taiwan)
The Emperor and the Assassin (Chen Kaige, 1998) (China/Japan/France)
Crouching Tiger, Hidden Dragon (Ang Lee, 2000) (Taiwan/Hong Kong/US/China)
A Tale of Two Sisters (Kim, 2003) (South Korea)