If you have a lot of Windows Media Audio (.wma) files, you will need to convert them into .mp3 or .m4a files before you can play them in iTunes. (iTunes will do this for you though.) Windows Media Player can directly play .m4a files.
Windows Media Player uses less memory than iTunes.
If you use MSN messenger, WMP gives you the option to display the title of your current track as your personal message.
Points for iTunes:
Built-in podcast support, which I don't think WMP has.
If you have an iPod, it would be more convenient for you to just maintain your library of music in iTunes and sync it with the iPod. It also allows you to directly play the music from the iPod.
At least on my computer, it doesn't stop responding as often as WMP does.
(All of the above is based on comparing iTunes 7.5.020 and Windows Media Player 11.0.5721.5230, which are the latest versions of the two players at the time of answering this question.)
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