I recently purchased cs3 upgrade version. Can I delete the older versions on my computer, or do I need to keep those on to allow cs3 to run correctly?

You need to keep CS2 to install the CS3 upgrade version but then I'm 99% certain you can get rid of CS2 once CS3 is installed.

Have a look in the Photoshop folder after you install. Adobe sometimes move older, now unused files into a folder, often called "Old Files" (if memory serves me) or something similar. Or is that filemaker??? Have a look anyway. Once CS3 is installed there should be no need to keep CS2.

Hugh