The small credit union I belong to uses a service to provide online banking, ATM connectivity and back-end computing support. They provide account access at any credit union branch that belongs to the service; they say there are over 6300 locations. As long as I have ID, the name of my credit union, and my account number (memorized) I can walk into any of those locations and get at my money.

My accounts are insured by NCUA, which is very FDIC-like.

It would probably be safer if I kept funds in a large national FDIC-insured bank as well, but I don't have enough money for that to make a lot of sense.