I've got a 15" Powerbook running Tiger, and if I leave it alone and on for a while, it locks up. Nothing responds and I have to hold the power button down to get it to shut off, then it reboots and everything is fine again.

Is there somewhere, like a system log that I can look and see what might be the problem?

Tiger is OS X 10.4.*, so there may be other stuff I've not seen.

check the System Prefs, Energy Savings.
You can set monitor sleep < system sleep but uncheck the box at the bottom
[ ] put HD to sleep when possible

also check the OPTIONS for whatever is appropriate.