There are three different ways to halt your Photobucket subscription:
Cancel recurring payments from within your Photobucket account:
Log into your account and navigate to the Account Status page. Just below your expiration date you will find a link to Stop My Recurring Payments. Clicking that link will turn off the recurring payments for your subscription. No further action required.
Cancel recurring payments via Paypal:
The steps to cancel recurring payments in Paypal may change from time to time. Please be sure to check their help site for the current steps to cancel recurring payments: Paypal Payment Cancellation Steps.
Non-Recurring payment accounts:
If your subscription is not set to renew automatically, you don't have to do anything in your account to have that subscription cancelled. After the expiration date your account will revert back to a Free Account.