You can buy bitcoins with paypal using a website here
https://www.virwox.com/The website primarily deals with trading in Linden Dollars (SLL). You can deposit your money using paypal, then buy Linden Dollars, then buy bitcoins with your Linden Dollars. For new accounts you often have to wait up to 48 hours to withdraw your bitcoins, but after your first purchase withdrawals are instant.
The website has this to say on the matter.
While most withdrawals to PayPal, Skrill, and Bitcoin accounts are processed instantly, we manually check some of them for security reasons (for example of new accounts). They will be processed within 48 hours
These are the currencies you can trade on the website that are applicable to bitcoin.
Linden Dollar (SLL)
EUR/SLL
USD/SLL
GBP/SLL
CHF/SLL
BTC/SLL
You can't directly buy bitcoins with ordinary money there, you have to buy Linden Dollars (SLL) first because they have no bitcoin/cash markets.
The high fees are the biggest drawback of this way of buying bitcoins, but bitcoin ATMs often have high fees too.