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Find an .avi and a .mov file. Mark them, choose File -> Get Info (or just hit cmd-I) and in the Info window under Open with set it to QuickTime Player, then hit the Change All button.
 
.mpg files should play just fine in quicktime player, I don't believe you need to do anything.

.avi files are often divx/3ivx compressed and need a special plug in or another media player such as VLC or Mplayer.

This topic has been discussed many times before, so if you do a search I'm sure you'll find your answers in full.
 
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