This is really intersting. It comes from the Public Goods and Externalities entry at the Concise Encycopedia of Economics. It is by Tyler Cowen. It should also be mentioned that Nobel Prize winner Ronald Coase wrote an article about this that appeared in the Journal of Law and Economics in 1974. So here is the quote from the Tyler Cowen article:
"Lighthouses are one of the most famous examples that economists give of public goods that cannot be privately provided. Economists have argued that if private lighthouse owners attempted to charge ship-owners for lighthouse services, a free-rider problem would result. Yet lighthouses off the coast of nineteenth-century England were privately owned. Lighthouse owners realized that they could not charge shipowners for their services. So they didn't try to. Instead, they sold their service to the owners and merchants of the nearby port. Port merchants who did not pay the lighthouse owners to turn on the lights had trouble attracting ships to their port. As it turns out, one of the economics instructors' most commonly used examples of a public good that cannot be privately provided is not a good example at all."