Gordon Brown talks about punishing bankers who have acted irresponsibly. About time, too. As taxpayers we are now all potentially supporting these banks with our own money, and it is right that we have a say in how they are run. Executives who have presided over their institutions like personal fiefdoms driven by ego and hubris have turned out to be architects of their firms' downfall. Why they are still in place is beyond me. At the very least, we should demand their heads.

Chief author of his bank's demise is Sir Fred Goodwin, who heads Royal Bank of Scotland and whose nickname "Fred the shred" reflects his approach to businesses he takes over. But "shred" could now equally be applied to the bank itself. RBS has never recovered from Goodwin's ego-driven deal to buy Dutch bank ABN Amro at the top of the market last year.

Goodwin is paid handsomely for his stewardship of the bank that owns the high street brand NatWest. Last year, he took home £5.4m in salary and bonus, and that was without his long-term incentive plan paying out. But his ambition to be a world leader has almost broken the 281-year-old institution. RBS paid a high price for Goodwin's obstinate pursuit of ABN Amro. Competition with his arch-rival John Varley, who runs Barclays, could have been a factor in his persistence. Varley had agreed a merger with ABN Amro before Goodwin came along to spoil the deal.

The RBS chief recruited partner banks to help him pay top dollar for the Dutch institution. He pursued the takeover against dissenting voices among his own shareholders - even after ABN Amro had sold the American assets he prized, and when it became clear the world had changed as the credit crunch took hold. The £47bn deal - the biggest cross-border banking takeover to date - was finalised late last year, just as banks were finding that sources of funding were drying up.

Nevertheless, Goodwin insisted the deal would be good for RBS, and that it could cope with the cost of its share of the takeover; two other banks were involved - one of which, Fortis, has now been nationalised by the Belgian and Dutch authorities. Six months later, as RBS reported its financial results, Goodwin stuck to his script about not needing to raise additional funds. But barely a month later he was asking shareholders for £12bn to boost the bank's capital. Of course, now RBS looks as if it will ask for government money too.

This unhappy record has seen Goodwin express his regret to shareholders after the bank made the biggest loss in its recent history earlier this year. RBS shares have fallen by nearly 80% over the past year. But so far he and the entire RBS board - five of whom earned bonuses of more than £1m each last year - remain in their jobs.

Barclays boss Varley, who fought with Goodwin over ABN Amro, had a lucky escape. But rather than learning a lesson about expensive international adventures, he is intent on building up Barclays' overseas operations. Its president, Bob Diamond, has been able to buy assets from the defunct American investment bank, Lehmans, to help turn Barclays into a force on Wall Street. Diamond, who was paid more than his boss, taking home £36m last year, wants to expand Barclays' trading and investment banking business. Whether this is a suitable ambition for a new era of austerity in the industry is questionable.

That brings us to the hapless HBOS, whose shares have dropped almost 90% in the course of a year, and which has had to be rescued by Lloyds TSB in a deal that flouts all existing competition rules. The youthful Andy Hornby, who runs it, also appears to be a leader for a different era. He was recruited from Asda 10 years ago, when banks believed they were retail operations and needed the skills of a marketing man.

Hornby, who tarted up the branches to make them more like shops and hired Howard, the singing bank manager for the group's advertising campaigns, is probably responsible for changing the way we think about banks.

While HBOS retrenched its mortgage lending early last year after it became worried about the housing market, it remains a major supplier of funds to large entrepreneurs and private equity companies. Hornby relies for much of his financing on the wholesale banking market, which has dried up. These exposures have spooked investors and worried other banks, who are wary of lending, forcing HBOS into the arms of the more staid Lloyds TSB.

Banks are supposed to be risk-averse institutions. They are custodians of our money, and we expect them to protect it. But it seems the current generation of bankers has forgotten this age-old adage and become carried away with the idea of turning their retail networks into international powerhouses. Now that gamble has not worked, they have come running to us to help them out.

In response we should start by insisting that these bank bosses pay with their jobs, and forgo the large payouts to which they will say they are entitled. This could be time to test their employment contracts in court. If Gordon Brown means what he says, it is time to hold the bankers to account.

deborah.hargreaves@theguardian.com