The most common cause of the pinwheel is doing virtual memory swapping. A system that pinwheels often is usually running out of RAM (think Linux pagefile slowness; same exact thing). However, a pinwheel that appears and then refuses to go away unless you shut down the computer often indicates an I/O error, a hard drive error, or a physical RAM failure. If the computer goes to access the swap file and then fails to do so because of a hardware fault, you will often see the pinwheel spin forever.
There are a few things I can suggest:
1. Look at the error logs. You can see the logs by using the Log Viewer application (it's in the Utilities folder in the Applications folder). Also look at the console using the Console app (same place).
2. Run an Apple Hardware Test. It should be on the DVD that was provided on your system.
3. Use Disk Utility to verify your hard drive and run a surface scan.
What you're experiencing *definitely* is not normal or expected behavior, and a problem as serious as the one you're reporting makes me suspect a hardware issue.
