I've used Paypal since they first arrived on the scene, long before eBay bought 'em up.
I have never had a problem with them. I authorized them to pull from my checking account. (same as using your debit card)
Paypal is a legit and secure site. It's not a new or fly-by-night operation. I feel completely safe using them. The convenience is fantastic and it's really great for overseas deals, as you don't really have to mess with exchange rates etc.
I use them every month for something. They're not just for eBay anymore.