Is there a way to install Mountain Lion on a Mac Pro 1,1 2006? The Mac Pro 1,1 2006 is not officially supported for OS X Mountain Lion, are there any work arounds to get it to work?

Your Mac must be one of the following models:
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Mac Pro (Early 2008 or newer)
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Yes its possible. The limitations that need to be over came are three fold. 


  There are two things that prevent 10.8 from installing on a MacPro 1,1.
  
  
  The first is the lack of EFI64. Mountain Lion as has no support for 32bit kernel and extensions so it will not boot. This is true of many early Intel macs.
  The other thing is that checks are made by the installer; against a supported machines list. If your mac isn’t on the list, it refuses to install.
  
  
  It’s important to note that an upgraded graphics card is virtually essential. The stock 7300 GT isn’t supported and will cause Kernel Pannic. I don’t think the X1900-xt is either, my 8800GT did odd things on DP1 but may be OK on newer builds. Ideally Id try and source a HD5770 or other newer card. 


Solutions:


  
  New compatible graphics card will need to be obtained.
  The first issue can be dealt with by using the Chameleon bootloader. Chameleon will emulate EFI64 and therefore load 10.8.
  Customization of the 10.8 Installer by adding your machine kind back onto the list of supported machines. 
  


Sources:


http://www.j4mie.co.uk/blog/2012/02/18/how-to-install-mountain-lion-on-macpro11/
http://www.jabbawok.net/?p=47