In New Zealand the bank that provides government departments with banking is required to provide "banking of last resort" facilities to people, even going so far as people who have (for example) done bank fraud. The facilities are minimal - no overdrafts or credit cards, obviously! - but provide enough to function in a society where cheques don't exist and cash is rarely used.
Canada has a funny approach: banks can pretty much close an account willy-nilly but they're also required to open up a basic bank account to anyone that can properly prove their identity. Not sure how far anyone has pushed that envelope.
