how important is the pre-emphasis stage in MFCC? I wrote a simple MFCC routine, using all the steps usually suggested in the literature with the exception of the pre-emphasis stage. How important is this stage?
 Also, some authors suggest that using rectangular windows instead of triangular doesn't degrade MFCC performance (as long as the windows are overlapping) so any ideas regarding this particular subject are welcome.
Pre-emphasis is a way of compensating for the rapid decaying spectrum of speech. The experiment is worth trying on real data - you will find that the DCT basis is better at extracting a set of decorrelated coefficients when the spectrum has been whitened by the pre-emphasis filter.

This justification does not really apply in the case of music where the spectrum is more slowly decaying - it is not uncommon in MIR papers to see MFCC computed without the pre-emphasis filter. In the case of music, an argument for pre-emphasis is that it provides a very crude approximation of the outer ear filtering. Some feature extraction modules are indeed using MFCC-like features with a proper outer ear filter (response given by Terhard's formula) in place of pre-emphasis - For example, it looks like this is what is used by the Echo Nest analyzer.