How would interest and fractional reserve banking work in a limited money supply? Suppose Bitcoin lenders (banks, creditors, investors) issue loans with interest. As the total supply of bitcoins approaches the 21M ceiling, the total amount owed in outstanding interest will exceed the money supply.

This is the same as existing banks: they actually hold only a fractional reserve of funds, and the economy as a whole owes itself more money than there is in existence.

The difference is that reserve banks can print more money (yes, with inflation). Bitcoin can't.

An economy can continue to operate, I assume as long as there is enough circulation for a debtor to pay back his interest. However, since interest is compounded, it grows at an exponential rate: over time, wouldn't the total debts eventually outstrip the coins in circulation available to repay them?

Would Bitcoin find itself in a situation similar to the current global economic crisis? How would it correct itself?
It doesn't matter very much because the economy can trivially create substitutes for currency. Anything that has the same capabilities as currency (fungible, easily exchanged, limited supply) can also serve as currency.

A good example would be a Mt. Gox code. Mt. Gox may or may not have 100% reserves, but it doesn't matter. A Mt. Gox code for 100 Bitcoins is basically as good as 100 Bitcoins. If you don't fully trust Mt. Gox, maybe it's as good as 99.5 Bitcoins.

Also, you can "print money" without actually being able to produce currency. For example, say I want to buy a car today and need 2,500 Bitcoins to do so. If someone loans me 2,500 Bitcoins in exchange for an insured IOU to pay 2,600 Bitcoins in six months, the 2,500 Bitcoins I borrowed to buy the car are still in circulation. But there is also now an IOU in circulation that is also worth 2,500 Bitcoins. As that note comes closer to maturity, it's value will go up. So just by time passing, the effective number of Bitcoins in circulation will go up.

This is bad news to the people who don't like the way a modern economy works, oppose fractional reserve banking and currency controls, and think that Bitcoins will bring on a new economy where banks can't create money. But I think it's pretty obvious that the same kinds of things will happen.

The whole Bitcoin system itself is an example of creating money out of thin air.