Today, that picture is changing. But some customers will pay a heavier price.
"Royal Bank of Scotland unleashes guerrilla assault on 'harbingers of doom' - shock." Though the headlines were not quite as dramatic as the one above, the bank's recent initiative on overdrafts marks a new stage in the battle for customers.
The attack on so-called "harbingers of doom" was aimed at senior bankers from Clydesdale Bank, RBS's local rivals, whose own soothsayers are forecasting the demise of free banking within the next few years.
Royal Bank disagrees. Instead of accepting defeat on this front, it has taken its fight for free banking into territory dear to the hearts of students, loss-making small businessmen and recent divorcees: overdraft fees.
From 1 December, all account holders have the chance to slip comfortably into overdraft with no arrangement fee or monthly service charge - just a relatively reasonable rate of interest, 1.25 per cent a month.
The biggest change lies in the scraping of a monthly fee - usually between pounds 5 and pounds 8 - still levied by most big banks on customers who go overdrawn, even when by agreement.
Pressing home the assault, the bank noted that for an authorised overdraft of pounds 500 which is used for one week every month, Lloyds Bank will take pounds 116 from its customer, Barclays charges pounds 80 and NatWest charges pounds 79. Bank of Scotland believes it deserves a grand pounds 142 for the service.
Royal Bank of Scotland will take a mere pounds 20.71 - only beaten by Midland with pounds 15.
Andy Marchant, head of current accounts at RBS, says: "Those who have forecast the end of free banking have completely misread the situation. Increased competition within the industry means that customers are receiving an even better deal.
"Most of our customers operate their current account within an agreed overdraft limit. We are recognising those customers who conduct their current account in a responsible manner and they will greatly benefit from our new policy."
Royal Bank's move runs against the grain of a convention in banking which is captured in the saying, "Owe a banker pounds 5 and you are at his mercy: owe him pounds 500m and he is at yours."
Traditionally, banks do not mind losing customers with piffling, unprofitable debts: if those customers stay, the interest paid may not cover the cost of servicing the overdraft. So they charge high rates of interest and levy fees for the administration work of confirming the overdraft.
Even in Royal Bank's case, this approach has not been entirely abandoned. It has financed part of its cost-cutting by boosting fees for unauthorised overdrafts. These have charges which sound more familiar: fees of pounds 15 a month. Interest is nearly double that of an authorised overdraft at 2.45 per cent, or a whopping 29.4 per cent APR a year. NatWest will hit savers with a pounds 50 initial fee, interest at 33.8 per cent APR and a frightening daily fee of pounds 3.50.
Other banks penalise unauthorised overdrafts in similar fashion. The reasoning behind the high charges is that banks regard unauthorised overdrafts as an irritation.
They present a greater risk to the bank because they can no longer have confidence that their customers will not draw more than a pre-agreed amount. So every single transaction has to be monitored. Instead of a note on a computer file, the bank has to waste staff time in monitoring the accounts.
Lesson: get it authorised. If a similar overdraft has been arranged before, a simple telephone call will usually suffice.
Banks with high charges for authorised overdrafts have mounted something of a defence to the guerrilla tactics of Royal Bank and Midland. They point to what has become known as the "pink" or "buffer" zone, an automatic overdraft, usually of pounds 100, which does not need to be authorised and involves no fees.
A spokeswoman for Lloyds TSB adds: "Charges and interest relating to overdrafts do not affect most customers as 70 per cent never go overdrawn.
"Overdrafts are a flexible form of borrowing which allow customers to dip in and out. The charges should be seen in the context of overall packages which include free in-credit banking and access to thousands of branches and ATMs across the country."
Here, Royal Bank is again injecting fresh competition into retail banking. Last week, it became the first traditional bank to offer its customers access to any of the 22,000 cash machines across the UK - free of charge.
So what lies behind this sudden burst of competitive fervour?
The answer lies in a fresh injection of energy to the banking sector - and a mushrooming number of new companies. Just when you thought the banking sector had been reduced to four - Lloyds TSB, Midland, NatWest and Barclays - new players are rushing in.
Halifax, Alliance & Leicester, Abbey National, Northern Rock and others have entered the sector. Fresh from making themselves popular by converting billions of pounds of members' funds into cash handouts, they mean business. One in four current accounts are now held not with the traditional providers.
Instead monthly wages go into the former building societies or Midland's telephone banking arm. Even those which have stayed as mutual building societies, such as Nationwide, are fighting for the same business.
A quick look at the overdraft fees of the new banks casts a fresh light on Royal Bank's initiatives: it only looks cheap next to some of its traditional rivals. For an overdraft of pounds 500 one week a month for a year, the same example as above, Halifax will charge just pounds 15.47. Abbey National only wants pounds 12.95. Alliance & Leicester has whittled it down to the cheapest rate of all - pounds 10.96 (see table above).
But even the new banks will not take kindly to customers who bust their limits. If a customer incurred a pounds 500 unauthorised overdraft for one week a month, Halifax would hit him or her for pounds 222.10 over the year.
The traditional banks are trying to fight back without further painful cost-cutting by offering enhanced service. Rather than slashing overdraft fees, Barclays prefers to do something which it points out could benefit all customers. It is piloting a new type of quarterly bank statement, tailored to each individual customer, to show all of their financial arrangements - mortgages, life assurance, pensions and credit cards - at a glance. So long as these arrangements are laid on by Barclays, of course. The big four high-street banks are determined, it seems, to fight back.