Here is what PayPal's sign in page says about security:

Keep your PayPal account safe and secure; here are some tips every PayPal member should know:
Log in safely whenever you access your PayPal account; open a new web browser (e.g. Internet Explorer or Netscape) and type in the following: (deleted by Mick)


PayPal emails will never ask you for personal information such as social security numbers, passwords, credit card or bank account numbers


Never download any attachments in a suspicious email
If you think that you have received a fraudulent email (or fake website link in an email), please forward the email (or URL address) to spoof@paypal.comand then delete the email from your mailbox. Visit our Security Center to learn more.