There are lots of great films, but the style of these films is often what is described as "arthouse". They are great works of cinema, but not always easily accessible to a general audience.In this genre I recommend:

Three Times - Hou Hsiao-hsien's beautiful film starring Shu Qi and Chang Chen. A love story across three times - 1911, 1966 and 2005

Rebels of the Neon God - Tsai Ming-liang classic about the life of Taipei youth in the early 1990s. 

Ill just recommend a few recent films which I think have artistic merit, but are more easily accessible.

Eternal Summer - this is a very powerful story about teenage relationships. It is unfortunate it never got much attention because it is a fantastic film.

Orz Boyz - wonderful story about children that will appeal to all age groups. 

Parking - dark comedy set in Taipei.

A few more worth a look are Island Etude, God Man Dog, The Most Distant Course and  1895.

A few interesting ones set to come out in the next few months are Yang Yang, A Place of One's Own and No Puedo Vivir Sin Ti. 

You liked "the wayward cloud"? That was a really odd movie, I didn't know what to think of it. For a Taiwan newbie, it might be a bit too much "culture", don't you think?

Note to self - Some of those are posted on the Taiwan Movie Guide, I should add the others.

Fili