In the New Yorker, James Surowiecki has written a good, concise history of the debt ceiling -- and why we should do away with it:

The truth is that the United States doesn't need, and shouldn't have, a debt ceiling. Every other democratic country, with the exception of Denmark, does fine without one. There's no debt limit in the Constitution. And, if Congress really wants to hold down government debt, it already has a way to do so that doesn't risk economic chaos--namely, the annual budgeting process. The only reason we need to lift the debt ceiling, after all, is to pay for spending that Congress has already authorized. If the debt ceiling isn't raised, we'll face an absurd scenario in which Congress will have ordered the President to execute two laws that are flatly at odds with each other. If he obeys the debt ceiling, he cannot spend the money that Congress has told him to spend, which is why most government functions will be shut down. Yet if he spends the money as Congress has authorized him to he'll end up violating the debt ceiling.