I have the criterion In the Mood for Love and want to get more. Can you recommend the best versions of his other films, Fallen Angels, As Tears Go By, etc...

AFAIK these are the best versions

As Tears Go By - Media Asia/Megastar
Days of Being Wild - Media Asia/Megastar
Chungking Express - Miramax
Ashes of Time - all dvd versions of this are pretty terrible.
Fallen Angels - Kino
Happy Together - Kino

As for Happy Together, get the R2 UK ... it even has the "Buenos Aires" making-of included as an extra.

Apparently the Korean version of Chungking Express has more extras than the Miramax version, but I have no idea if that's true or not. It's the same Rolling Thunder cover and the same DVD.

As for the rest, I'd follow Fandango because I have no idea.

Apart from "Chungking Express" R1, I'd recommend for you to wait.

Wong Kar-Wai is currently working on remastering most of his films. There is a rumor of an extended Ashes of Time, as well as a definitive version of the Happy Together DVD (similar to R2, but better).

On the other hand, maybe not wait, considering how long it takes him to do anything....