Investors are feeding a dramatic world-wide slowdown by trying to flee it, racing away from many corners of the globe they used to favor. The resulting tumbles in stocks and currencies have helped provoke a broader crisis in places such as Iceland, whose turmoil in turn is hitting bank depositors from London to Amsterdam.

As foreign capital flows out of a host of smaller economies, it's laying bare the excesses built up during five years of strong growth and easy access to borrowing. Concerns are rising that such countries...