Let me guess, they paid with a credit card? I just had this happen too. Did they have a "confirmed" shipping address? Here's a couple of solutions:

Go to your PayPal account and specify not to accept payments from unconfirmed addresses.

Also tell it to refuse payments from people using a CC, when they have a bank account.

Tell PayPal not to insert their logo in your auctions.

In your auctions specify that you will not accept CC's, only PayPal balance, or bank transfer.

Request the buyer's info from eBay. This will send them a form letter letting them know you requested it. It starts them wondering. On the down side, it also gives them your contact info. If you were smart when you signed up, you have a fake phone number in there!

Go ahead and start filing all the fraud investigation paperwork with eBay and PayPal.

File for your eBay listing fees under the non-paying bidder clause.

Leave negative feedback for the buyer, and block the buyer from bidding on your auctions ever again.

If you've already left feedback, and they you. Comment on the feedback they left you adding that they used fraudulent funds...etc.

Sorry I couldn't be of any real help, but once it happens, there's not much that can be done.