Sure, apps do crash, sometimes annoyingly so. That was certainly the case with OS 9 and before, the difference now being it doesn't bring down the whole OS in the process.

Err, nope. The difference now being it doesn't always bring down the whole OS. The whole OS still falters plenty.

I'm thinking you have a hardware problem.

Same here. We've had seven Macs in our home since OS X came out and, collectively, haven't experienced but about 4 kernal panics. That's not unusual, from what I hear on boards around the net.

Random KPs point to hardware problems indeed:
You might want to run Apples hardware test, check your RAM with memtestosx.org and make sure that your files are ok with applejack.sf.net.

A flaky PSU is another possibility among lots of others, but you definitely have quite a bit covered once you're done with the three suggested above.