I believe that, in a way, political parties are natural outgrowths of the democratic process. Obviously, a single voter on their own will not be able to sway the machinery of government in a nation of 300 million. Even at the state level, a single vote is relatively insignificant.
But when a voter bands together with other voters, they become a force to be reckoned with.
The incentive for individuals seeking a certain result from a large system is to pool their efforts with like-minded fellow citizens. This is essentially what a political party is. Nothing more than a group of people saying, "We agree enough on enough of the issues to stand together as one and demand action."
Political parties also have the added benefit of bringing people into a coalition around an issue that they may not personally have otherwise engaged on. There are many issues in the Democratic Party platform that I don't have a particular, personal passion for, but I support them because they are supported by people who join me in support of issues I do care about and because after being presented with issue, I find their case persuasive, even if I still lack a personal passion for it.