So, a couple of years ago I gifted my parents Netflix paid for on my BofA debit card. When I changed my name I received a new card with a new expiration date (didn't even realize the date change).
My parents received a notice from Netflix (I don't get the notices because it's my parents account that I just happen to pay for) that my card has expired. They called to tell me that their account has ended because of this. I was a bit confused because I looked at my bank card and it doesn't expire until 2013. All well. So I told them that I hoped they enjoyed it but now I'm poor so I won't be renewing it. They were fine with it, no big deal.
I looked through my online statements and realized that for July and August I was charged for the account that was no longer in use (the Netflix account, not my bank). WTH?!
Netflix informed me that because it's a recurring payment, even though the card is expired, if the account is still in good standing they will keep charging.

It's apparently a protection thing Visa does. Who knew!
So, word to the wise, if you get a notice saying that your card has expired and think that means you account is canceled with that company, just call and make sure.
Ignorance is a poor defense.