I think this has to be done extremely carefully - we don't want governments interfering too much in the operations of companies but it is clear that something has to be done.

My own personal scheme is that some public body would monitor companies and try to identify those that belong to the "too big to fail" category. If any organisation falls into this category then the executives of the organisation would be notified individually that if the organisation fails and has to be rescued using taxpayers money that they personally would be on the hook for all of their assets. It would then be up to the executives to reduce the size of the company, e.g. by splitting into smaller organisations that would be under the threshold, or accepting the risk if they believe their organisation is perfectly well run.

Of course, there are a lot of problems with this scheme - notably that banks would simply incorporate somewhere else, but something like this has to be put in place or the same thing is bound to happen again.

[Edit: In one of Vernor Vinge's short stories he has Earth being conquered by an alien race whose only form of central government are officials who have the power to order any organisation to be split up if it becomes too powerful.]