I should be able to go into my bank or card service online. View a list of all my subscriptions. Click on a subscription (or select all). And cancel.
If there is a card that offers this let me know because I'll be switching immediately.
Thats how it works in India: all your "repeating" charge authorizations show up on a portal maintained by the issuing bank. All services that charge via these authorizations send an SMS alert before they debit the next charge. At any time, you can go into the portal and cancel any of these authorizations. No need to talk to the charging co at all, though still, best to first cancel from them. Jus that they know its trivial for the user to go and cancel the auth, so no one makes it difficult to cancel.