Could be many things, we should start with this...
"Try Disk Utility
1. Insert the Mac OS X Install disc, then restart the computer while holding the C key.
2. When your computer finishes starting up from the disc, choose Disk Utility from the Installer menu at the top of the screen. (In Mac OS X 10.4 or later, you must select your language first.)
Important: Do not click Continue in the first screen of the Installer. If you do, you must restart from the disc again to access Disk Utility.
3. Click the First Aid tab.
4. Select your Mac OS X volume.
5. Click Repair. Disk Utility checks and repairs the disk."
Then try a Safe Boot, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, reboot when it completes.
(Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive.)
See if the Disk is issuing any S.M.A.R.T errors in Disk Utility...
Open Activity Monitor in Applications>Utilities, select All Processes & sort on CPU%, any indications there?
How much RAM & free space do you have also, click on the Memory & Disk Usage Tabs.
Open Console in Utilities & see if there are any clues or repeating messages when this happens.
One way to test is to Safe Boot from the HD, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, Test for action in Safe Mode...
Reboot, test again.
If it only does it in Regular Boot, then it could be some 3rd party add-on, Check System Preferences>Accounts>Login Items window to see if it or something relevant is listed. Also look in System Preferences' Other row.
Also look in these if they exist, some are invisible...
Thanks! I'm going on a 2-week trip, but will try this when I get back. I repaired permissions already, but not by booting from the install disk. Also, I have only 1 GB of RAM, so will check memory usage, among the other things that you suggested. When I try to access other user accounts from the icon on upper right, it seems to search for but not find them.