iMac freezes often - running Snow Leopard

We've seen a troublesome issue occur since upgrading recently to Snow Leopard. The iMac will freeze at random times. The mouse pointer simply stops moving - no spinning beachball. The keyboard also becomes inactive during these freezes. The only recourse is to reboot... which solves the problem... for a while. Within a few hours... and totally at random... the mouse will freeze. It doesn't happen when the mouse is moving, just after periods of inactivity (sometimes just minutes of inactivity - not enough time to initiate the screensaver).

I did boot the computer into Safe Mode and the freezes did not occur for two days. As soon as I booted back in normally, the freezes occurred within 2 hours.

Any ideas greatly appreciated.

Thanks,
~Rick