The folks at Baseline Scenario have a nice walk-through of the problems the banks are facing and the possible fixes. They imagine it Lord of the Rings-style with a "Bank of Middle-Earth" stuck with toxic assets.

Option 1: Bank Mitosis : Bank of Middle-Earth splits into a good bank (Bank of Gandalf) and a bad bank (Bank of Sauron)

Option 2: Little Red Riding Hood fix: Create a "Big Bad Bank" for the bad assets.

As they explain, both solutions have problems.

It's worth mentioning that we're not really in new territory here. The International Monetary Fund deals regularly with countries that have to fix up their banks. Sweden managed it just fine.