It doesn't sound like the normal Windows Update downloading icon, but it could be P2P like Limewire, bitTorrent, uTorrent, etc.
What about any 'anti's', like anti-virus, anti-spyware utilities?
What happens if you double click that icon?
In my icon tray on the right side of my taskbar, I have a small square with a cirled red arrow moving clockwise. When I move my mouse over it it says downloading. What exactly is it downloading. This has been going on for a couple of days. Any information would be greatly appreciated. I am running Windows XP on a network computer at work. There is only one other computer linked to mine and this is not happening on the other computer. I have never seen this before and I would really like to know what it is. Thank you.