Paypal (R) has this to say about their security:

The security of your information, transactions, and money is the core of our business and our top priority at PayPal.

PayPal automatically encrypts your confidential information in transit from your computer to ours using the Secure Sockets Layer protocol (SSL) with an encryption key length of 128-bits (the highest level commercially available). Before you even register or log in to our site, our server checks that you're using an approved browser - one that uses SSL 3.0 or higher.

Once your information reaches us, it resides on a server that is heavily guarded both physically and electronically. Our servers sit behind an electronic firewall and are not directly connected to the Internet, so your private information is available only to authorized computers.