From the earliest period of American politics, with Federalists and Antifederalists competing to create the government, to the modern day Democrats and Republicans who compete to reshape America's foreign Policy, among other issues, political parties have been an influence.  Additionally, political parties help people to get elected to any given position in the US Government, that voters vote on.  The latter of the two idea's, that political parties help people to get elected is, was, and will continue to be a major factor in determining how influential a party is.  
	One of the major things that a political party can provide to help someone gain candidacy and eventually a position, is money.  The parties provide money to candidates that they feel have a chance of winning an election.  With money, a candidate can run an ad campaign, travel around to various locations, hire consultants, and anything else that they will need.  In exchange for receiving money from a particular party, a candidate, if elected, will then vote in favor of the party, or implement policies that are favorable towards the parties stance on a particular issue.  One of the main reasons money is so influential in politics, other then it being money, is that without it, unless the candidate has a large amount of private money, they would not be able to run for office to a successful end.  
	An additional reason as to why political parties still have influence over elections is name recognition.  On average, 40% of voters vote for the same party no matter who the candidate is.  Because of this, if a candidate is identified as belonging to one party or another, that's 40% of the necessary 51% for a majority gain election - assuming it's a 51% threshold needed for a majority.  With the support of 40%, then getting another 11% is easier then getting 51%.  Even if the total is not as high as 40%, the added bonus given by having party recognition can help contribute to a person getting elected, or not get elected if the party's getting bad press for a particular reason.  
	Because of their ability to donate money to candidates and to get name recognition for a candidate, political parties still have a large amount of influence over elections and are still relevant in modern times.