If the bank that issues my credit card goes bankrupt, do I still have to pay?

The account (if you carry a balance) will be sold as a receivable. However, it will convert to a closed-end loan.. The rate will not change, unless you pay late. Thus, no more using the card. Reason being the first 6 digits on the card are the BIN, Bank Identification Number. Visa/MC's systems will not function properly if one bank is managing cards issued with multiple BIN's. Even worse, the system would melt down if one BIN was used by multiple banks. The entire routing of transaction information to move money needs this one-to-one relationship.

Target National Bank and Target Stores are separate. If one part goes bankrupt the other will continue to be in business. GE Money Bank and General Electric have a similar setup I think. Not paying credit card bills will damage your credit even if the bank goes bankrupt.