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What type of files will I be able to play/stream?
It is unknown at this time, as no in depth information is available, however the Media Center Extender portion will at very least be able to stream WMA, MP3, WMV, MPEG-1, and MPEG-2.
Can the Xbox360 Play Divx and Xvid files?
While the officially supported file formats are currently unknown, most likely the 360 will not have the ability to use new codecs not provided by MS; meaning no you probably wont be able to play Divx or Xvid files. Most likely you'll be limited to the same formats natively supported by Windows Media Player.