Apple has posted an official list of supported hardware on its OS X 10.8 Mountain Lion “How To Upgrade” page.
In order to install and run Mountain Lion, your Mac must be one of the following models: iMac (Mid 2007 or newer)
MacBook (Late 2008 Aluminum, or Early 2009 or newer) MacBook Pro (Mid/Late 2007 or newer)
MacBook Air (Late 2008 or newer)
Mac mini (Early 2009 or newer)
Mac Pro (Early 2008 or newer)
Xserve (Early 2009)
Presumably, anything older than the models listed is excluded because of 64-bit compatibility issues – at least the right sort of 64-bit compatibility (OS X version 10.8 is a 64-bit-only operating system that won’t boot in 32-bit mode) – and/or insufficient graphics processing power.
If you’re running OS X 10.7 Lion, you can find out if your current Mac qualifies by clicking the Apple icon at the top left of your screen, choosing About This Mac, then clicking More Info.
Note that Mountain Lion will install over OS X 10.7 Lion or the latest version (v10.6.8) of OS X 10.6 Snow Leopard. While you have the About This Mac window open, you can check what version of OS X your Mac is running.
If you are running Lion (10.7.x), youre ready to update to Mountain Lion. Go to Step 3. If you are running Snow Leopard (10.6.x), update to the latest version of OS X Snow Leopard before you purchase OS X Mountain Lion from the Mac App Store. Click the Apple icon and choose Software Update to install Snow Leopard v10.6.8.
With the above provisions satisfied, you’ll be ready to download OS X Mountain Lion from the Mac App Store when its available later this month. Open the Mac App Store from your Dock to buy and download Mountain Lion. Then follow the onscreen instructions to install it. If you don’t have broadband INternet access, you can visit any Apple Retail Store to get help with downloading.
For full details, see: