Yes, USB drive viruses do exist.
No, you do not actually need to run a file for malware on a USB drive (or Kindle) to jump to your computer. You just have to plug it in.
Back in 2008, the DoD banned USB drives for this very reason. The story I heard is that "someone" (almost certainly Chinese spies) dropped a few USB drives in DoD parking lots. People picked them up, plugged them in to see whose drive it was, and got zapped.
That said, I don't see Kindles as being a particularly big risk, unless you're plugging your Kindle into a wide variety of computers. And you should always run antivirus software. Well, on Windows anyway.
