Will Mountain Lion run on an early 2008 MacBook White?
As Steve Moser says there is no support for 32 bit drivers and Mountain Lion will refuse to install on the macs which had 32 bits drivers (someone seems to be too lazy to rewrite them?).

If this answer is not the one you want to hear, then you can install Mountain Lion the hard way. Because there is a way (which worked for the preview).

You will need another compatible mac (support) and you will have to do some hard drive switching.

The idea goes as follow:


Get Mountain Lion
On the target Mac remove the hard drive (target drive)
On the support Mac insert the hard drive (USB or internally)
Install Mountain Lion on the target drive
Put the target drive back in the target Mac
Boot on the target drive holding Cmd + V And write down the ID given in the error message "Incompatible Mac detected: ..."
Put the target drive back to the support Mac and on this drive in /System/Library/CoreServices edit PlatformSupport.plist


Add your board ID in the SupportedBoardIds section.
Add your model ID in the SupportedModelProperties section.

Put the target drive to the target Mac
Boot


You should be able to get to the desktop but without hardware graphics support.

To enable the graphics hardware support you will have to install the right kernel extentions. You could use kexthelper.



EDIT: To avoid all the hard drive switching and messing with internal components you can boot the target Mac in the so conveniently named "target mode" and connect it to the support Mac on which you could install the OS to the target drive and then boot on the target drive to edit the plist files.