Although the credit card companies and PayPal are much better at removing these items, they are a common "terms and condition" that require you to affirmatively cancel an account to prevent renewals. They are called "negative option billing" and many companies hide this language pretty deep into the terms. You were smart because you kept the notification setting from PayPal to alert you to a debit against your account, so you didn't have to just stumble upon it when reviewing your list of transactions (which most people don't do).

I try to avoid automatic billing even with known companies. Years ago we had our phone bill automatically paid from the checking account. One month we saw a charge for nearly $4,000 in telephone switching equipment billed to the account (and deducted from my checking). We looked into it, and someone had fraudulently used our telephone number to process shipment of equipment to a building in Detroit.

I sought to reverse the charge - no luck. I sought to cancel the shipment - no, I couldn't do that because I didn't order the equipment. Talk about a bureaucracy! We only got the charges refunded because my wife happened to work in the legal department - at the phone company. The next guy wouldn't be so fortunate.