There are several ways for saying why. I'm trying to decide when each is appropriate. Based on watching various films...
なぜ I've only heard this one occassionally, in a 'Why is this the case' type situation.
どうして Heard quite a lot. More 'What is happening' I think. どうしてんですか。is 'What's wrong?'
なんで Also heard quite a bit. Probably 'What for', If I responded なんで to 買いましょう would the meaning be 'For what are we going shopping' or 'Why are we going shopping'?
Keeping on with the shopping theme. If I responded to 買いましょう with なぜ would the answer be たべものがありません, while if I responded なんで would the answer be along the lines of 白米や海苔や漬け物を買いたいです。If I replied どうして would the answer be something like 買いましょうって聞いてください。All very polite. (I wonder what the japanese equivalent is for 'cloth-ears', but I digress).
Alan