Chungking Express
One of the most memorable films I've watched. I had no idea the female lead in the second part was Faye Wong, until someone else told me. What a zany performance!
According to the various critical reviews, if this film is approached from a plot/story perspective, then it's a little confusing. There's some truth in this, not the least in the "link" between the two distinctive plots in the film. Also, there are some discontinuities in time, and one has to close them by assuming a "time leap", which I did a couple of times in the second part.
Here's a clip from the film, set to Faye Wong's cover of The Cranberries' Dreams:
