My main complaint about Windows Media Player would be its performance (especially the working set).
I used Winamp from version 0.x to this day. What I particularly enjoy about it is the fact that it really allows you to "pay as you go". In Winamp 5, if I disable all the shiny features, I get a working set as small as the one in v1 or v2.xx (I can prove that
with vadump logs or perfmon logs if you wish).
That never happened with WMP (I'm still evaluating v10 though). V9 sucked big time, it's painful to get rid of all the useless shiny features and you get no real benefit, the working set is about the same.
The second complaint would be about usability. Previous posters have made a good job complaining about this so I won't do it again.