Unquestionably, third parties do not work in the United States, and only serve to elect a candidate who otherwise would not be elected. A clear example of this is the 1948 election in which Strom Thurmond ran as a third party candidate on the States Rights (Dixiecrat) ticket. Harry Truman was projected to lose the election; however those who voted for Thurmond otherwise would have voted for Truman's opponent, Thomas Dewey, which deprived Dewey of a number of electoral votes. The end result was the election of Truman.
Nor is this the only example. In the 1848 election, Zachary Taylor defeated Lewis Cass for the Presidency when the anti-slavery vote was split between Cass and Martin van Buren who ran as the candidate for the Free Soil Party. In the 1892 election, the Progressive (Populist) party candidate, James B. Weaver deprived the incumbent, Benjamin Harrison, of just enough votes to assure a plurality--and electoral college victory--for Grover Cleveland.
It was for this reason that Sen. Kerry begged Ralph Nader to remain out of the 2004 Presidential election--he saw the handwriting on the wall. Then too, the presence of Ross Perot in the 1982 election assured the election of Buill Clinton over the incumbent George Bush. Arguably, the same thing happened to Al Gore in 2000. In each instance, the third party candidate proved to be a spoiler.
Bottom line, until the U.S. adopts a system of coalition governments comprised of three or more parties, the U.S. political system is not conducive to third party candidates or parties.
The contributions of third parties are mostly in the eye of the beholder. Some people would argue that they contribute nothing while others would say they make the system more democratic.
You can argue that the presence of such parties makes our system more democratic because it gives people more choices. For example, if this year's election were to come down to Mitt Romney against Barack Obama, there would be much less of a variety of ideologies among the candidates than there would be if Ron Paul were to run as an independent. If Paul did run, libertarians would have a greater chance to have their voices heard.
However, you can also argue that third parties only serve to spoil the chances of one of the other candidates. A Paul candidacy would make it much more likely that Obama would win a second term. Similarly, Ralph Nader's candidacy in 2000 can be fairly directly credited with allowing George Bush to defeat Al Gore.
If third parties contribute anything, it is an increase in the choices available to voters.