For an example, all of the people in New Orleans whose houses were flooded and did not have insurance. Are the owners just stuck with a ruined house and the mortgage if they cannot afford the repairs?

They are out of luck, they still have to pay.

Unfortunately in many cases the answer is 'yes'. A mortage is just a name for an amortized loan and is, therefore, a promise to pay. In the New Orleans situtation, some banks are forgiving these debts or working with people to help them with alternative payments, but many people are left to finish paying mortgages on homes that do not exist. Just because something is destroyed or consumed before the terms of a loan come due, does not mean the loan should be automatically forgiven. Imagine buying a calculator with your credit card and losing it the next day. You still owe your credit card company. The same applies to mortgages. But again, banks are ultimately run by people, not pure heartless economic theory (not to mention they have public images to maintain), so many of them are coming up with creative solutions. I would advice you go to the website of individual banks and mortgage firms, click on their FAQ and see how they deal with catastrophes.