We are a republic, which is a representative democracy. There is no country in the world that is a pure democracy, where the citizens vote on every issue. But we are the only republic in the world that I know of where the winner of the popular vote, can lose the election.

"Even if the American president, as in most other democratic countries, was elected by popular vote, the United States would still be a representative democracy, not a pure one." 

http://prospect.org/article/indefensible-electoral-college