Paypal, which use to be a seperate company from Ebay, is now part of Ebay and makes the payment of Auction's a much easier and simplier process.  Ebay has assured it's members that this method of payment, using your checking account or credit card, a safe and secure method.  It allows a winner to immediately pay for an item using their bank account or credit card safely and not send any account numbers to the seller.  Ebay/Paypal maintains the site in this secure mannor. 

In the past, prior to Ebay's purchase of Paypal, several folks had experienced less than satisfactory transactions.  Personally I joined the Ebay family of users in 1997, and Paypal not long there after.  I have never had a problem.  I highly recommend logging into either site and safely registering.

A word of caution, never answer or give information to any email received from what appears to be Ebay or Paypal.  Ebay nor Paypal will send you anything where you must answer from a link.   Always log on to the appropriate site to see if it is real.  Any simple email that starts with "Dear customer", are always "spoofs" and are "phishing emails" trying to get your account information.  If you feel that you have fallen for one of these "spoofs" immediately go in and change your passwords to stop any fraudulant attempts on your account.

Always check your account for unauthorized entries and/or changes in your passwords.  If you suspect this, notify Ebay immediately at security at ebay dot com.  If you receive a "phishing" email, do not answer it.  If you suspect it is a phishing message,  forward it to spoof at ebay dot com so that Ebay can investigate it and take action against the senders.