Look at your panic logs in Console (Applications > Utilities > Console). This will give an indication of what was happening when the panic occurred.
If there's some kind of regularity to the panics - e.g. the same kext is causing every panic, that usually means the hardware related to that kext (like your wireless card, your hard drive, the GPU, etc) is causing the panic. If the panics seem completely random, it's more likely that either the hard drive or the RAM is failingIf you're close to an Apple store, I'd make a genius bar appointment and ask them to run diagnostics on your hardware. If you still have the discs that came with the computer, you can boot the diagnostics CD and run the Apple Hardware Test, which will allow you to run a diagnostic on your RAM.