According to the tech specs, I have an early 2008 Mac Pro, and I'm running 10.6.8, so it should work. The problem is that I can't actually download it from the App Store, which keeps freezing on me. When I click either "buy now" or "update", I get the spinning beach ball of death. Perhaps it would be possible to update the App Store application?
It also freezes when I click on updates.
Check the startup disk using Disk Utility. The startup disk may need repairing.
Launch Disk Utility located in /Applications/Utilities
Select the startup disk on the left then click First Aid.
Click Verify Disk. If necessary, click Repair Disk. You will need your Mac install disc to proceed.
While you have the Disk Utility window open check Available and Capacity at the bottom of the window.
Make sure there's at least 15% available disk space. Mountain Lion is a 4.35GB file.