I remember reading that early on in the U.S. election process, the Vice President was the losing party's presidential candidate. The thought process was that it would bring more moderate political views into the government, rather than leaning heavily one side or the other. But now, presidential candidates nominate their own vice presidential candidates, almost entirely from their party. When did this change occur? What were the reason behind the switch? What effects did it have on American politics?
The change has its roots in election of 1800. In this election Thomas Jefferson and Aaron Burr, although running together, received the same number of electoral votes (73). Per Article II, Section I of the Constitution, the election went to the House, where each state held a single vote. A candidate must receive a simple majority of all states to be elected.
The states deadlocked for thirty-six ballots and nearly a week, with Jefferson winning eight states, Burr winning six, and two states, Vermont and Maryland, abstaining. On the last ballot, these delegations filed blank ballots, giving Jefferson the White House.
Following this experience and the hot mess it created, Congress proposed and later passed the Twelfth Amendment to the Constitution, ratified in 1804. The Amendment states that the Electoral College now casts two separate votes for President and Vice President (which cannot come from the same state).
Nowadays, you'll see vice-presidential candidates that are picked to "balance the ticket" geographically, demographically, or ideologically. For example, Northerner John F. Kennedy tapped Southerner Lyndon B. Johnson to run with him in 1960, a geographic balance (and perceived as a ideological balance as well given what "Southern Democrat" meant at the time, although Johnson would end up signing the key civil rights bills of the era).
Here's a nice piece on contested elections in general and the struggle the Founders faced to build an electoral system.