MOV files can contain video and audio coded with many different codecs. Its the same with AVI files. Use Mediainfo or Gspot to find out what the technical details of the file is.
1st - what version of Quicktime do you have installed?
2nd - more on what Andrew asked
Read Bill Hunt on a file type as WRAPPER http://forums.adobe.com/thread/440037
What is a CODEC... a Primer http://forums.adobe.com/thread/546811
What CODEC is INSIDE that file? http://forums.adobe.com/thread/440037
Report back with the codec details of your file, use the programs below... A screen shot works well to SHOW people what you are doing
Welcome to the forum.
Along with the comments by others, do you have the latest version of Apple's QuickTime Player installed on your computer?