A: If your machine had a completely erased hard drive and a fresh install of OS x 10.6 (no other software installed) and you got kernel panic's then it's the 10.6 disk, you'll need to clean it or get a new one from Apple.
If the new disk also produces the same problem, then it's got to be the hardware.
B: If your machine is like A, but the kernel panics started when you updated to 10.6.8 (no other software installed) then it's a bad update. Reinstall with the 10.6.8 Combo Update instead. Also c boot off the 10.6 disk and Repair Disk, the 10.6.8 update did something to the drive that it needs repair.
C: If your machine was fine on 10.6, installed third party software worked, then kernel panics started after the 10.6.8 update. Then it's compatability issues with kext files and 10.6.8 changes.
The 10.6.8 update borked a lot of third party kernel extension files (kext) installed in OS X.
What you can do is this:
Hold the Shift key down to boot into Safe Mode, this will disable the kext files from loading, backup your files off the machine (not TimeMachine) and disconnect all drives.
Go around and update all your third party software so it's compatible with 10.6.8,
If you need a clue, look in your System/Library/Extensions and usually the names of the companies are on the kext file names. Sometimes copy protected software will use another companies copy protection system, so it will be under another name.
Funny thing about kext files, they are not all in the System/Library/Extensions folder to load upon boot, they can be located anywhere the program decides and loaded when the program loads.
If you have programs that are auto-launching at log-in then naturally so does it's kext files.
10.6 will run all your present software and drivers for hardware just fine, 10.7 will not and is NOT advised for older hardware. Early 2011 or later Lion is just fine, but you'll likely have to buy all new software to work with it.
Despite 2GB of RAM being Lion's minimum, 4GB is advised. Also you will need a 64 bit Intel Mac, not a 32 bit Intel Mac (no Lion for Core Duo's)
Tested, Lion is a hair slower than Snow Leopard
Check this site to make sure your third party programs are updated for Lion, not many are yet.
Some are undergoing a rewrite because Apple introduced a MacAppStore and likely told all the developers their programs will eventually have to comply with the restrictions placed there to run on Apple hardware, this means Apple is likely going to close up and we can't install software of our choice just like it is on iPads and iPhones.
http://roaringapps.com/apps:table