The right - and the obligation to open one (fees are normally not high). No salary should be paid in cash - and social benefits only to accounts. How much could be saved - and how much crime avoided.
In the past banks did turn down customers who were considered risky and being unprofitable. With direct debit cards and automation the risks and costs have been lowered so much that these arguments are not acceptable. In most countries it is already now
almost impossible to lead a normal life without a bank account. In the future it will be even more so - in all countries.
Good article here: http://www.economist.com/node/21530164