This is default Windows XP behaviour for anything it classes "Removable Storage", which includes all USB devices. What I typically do is install the Microsoft TweakUI
PowerToy, and fix that and some other things.
I hesitate to ask: why copy the whole of C: to it? If you know where your data is, you'd be better off just backing up the data. A full copy from C: is not a good backup strategy - you're copying a lot of system stuff that's no use to you in the event of a problem.