As far as I know, Paypal is extremely secure and has worked hard at keeping it that way. They bought Verisign specifically so they could implement their security procedures into their own systems.
That said, I have heard horror stories from people who relied on Paypal to manage their own web-income, i.e., they take forever to credit accounts, and if you lose access for whatever reason (say, your account got mistakenly blocked because of a fraud charge investigation), Paypal makes it ludicrously difficult to verify your identity and regain access to your money.