Joshua Spivak, in USA Today (July 7, 2004):

... So why do we even have a vice president? The position was not created to help balance an election ticket, nor was it intended to provide the president a surrogate for state funerals. Rather, it was an almost-accidental afterthought.

Under the rules of the original Constitution, each presidential elector was granted two equally weighted votes, which could not be cast for candidates from the same state. In order to make the second vote meaningful, the person who finished second would be the vice president. If the president were to be the best person for the job, then the vice president should be the second-most-capable person. What the constitutional conventioneers hadn't intended was that political parties would quickly reshape electoral politics.

By the fourth national election in 1800, the nascent party system exposed the design flaw. A tie vote between Thomas Jefferson and Aaron Burr resulted in the House of Representatives deciding the presidency. After his victory, Jefferson's Republicans passed the 12th Amendment, which required a separate vote for the president and vice president. Stripped of its original position as a job for the runner-up for the presidency, the vice presidency fell into obscurity.

Without its prestige, a mostly motley collection of third-tier politicos were chosen for the No. 2 job, primarily to gain convention support for the presidential candidate.

The rehabilitation of the office began with Harry Truman, who assumed the presidency in the waning days of World War II with almost no preparation for the immense job before him. Truman saw to it that Alben Barkley, his vice president after 1948, would be at least somewhat prepared, and he made the VP a member of the National Security Council. Subsequent presidents have added substantially to the vice president's portfolio. This has reached its apex with Cheney, who has been cited as serving in a prime-ministry role.

However, the reasons for the resurgence involve more than good policy. Political considerations and changes in how we elect presidents play the major role. Previously, state leaders and machine bosses decided who would be the parties' nominees, frequently in the backrooms of political conventions. The vice president would then be an addendum, usually a sop to the losing side....