This literally just happened to me today, and it was a bit of a pain, but it only took half an hour with last month's statement and a web browser to update all

This literally just happened to me today, and it was a bit of a pain, but it only took half an hour with last month's statement and a web browser to update all my regular payments. The one thing I would recommend is having a secondary card with a different provider kept as a backup, just to deal with the couple of days between cancellation and receiving the new card. Even better is if it's a different card type (Visa if you have a MC or whatever) for that once in a blue moon situation when a merchant doesn't accept that card. Finally, if you do this, put some regular, low value monthly payment on the backup card so it doesn't get cancelled for inactivity. Netflix is good.