Older iMac with Snow Leopard hangs

I have an iMac, model 6,1 with Snow Leopard, that occasionally hangs. I might click on an application (iPhoto for example) in the dock and the icon expands and it stops right there or when an application first starts, its window is displayed on the screen but never gets completely filled and it hangs there. Can't force quit because the keyboard and mouse are inoperable. BTW, both keyboard and mouse are wireless. Only solution so far is to power off and power on. Then it runs fine for several days. I have run disk Utility and it indicates the disk is OK.
Has anyone else seen this condition?

The symptoms you describe can possibly be attributed to bad or failing memory or a problem with the graphics processor.

Perform the Apple Hardware Test with your original install recovery DVD that you received with your iMac. Run the extended tests. There is also the free MemTest for OS X which you can download from here.

Thanks chscag.
Tried both suggestions. No problems found. Don't know about the video card. I've had no visible problems with it though, so I think it is OK.