Although many perceive that our government is a democracy, it is not; therefore, what type of government do we have?
We have a republic, a representative democracy, at least on paper in the Constitution. But in practice, I believe it is more like an oligarchy, a government by a few wealthy and privileged individuals who work very hard to maintain the idea that it is still a very democratic process. We used to have the media to vet these individuals for us, but the Fourth Estate has largely fallen by the wayside in terms of truly informing the people about candidates and elections.
Our government is a republic, because we have elected representatives. Therefore, it is not a pure democracy. It is not true that any person can be elected either, because the electoral college is a compromise. People cast votes, but their representatives are the ones that actually vote for the president.
Really our government is a federal repubilc because it is a union of states with a republican or representative form of government. The term "federal" refers to the central government. The states also maintain an independent sovereignty while submitting in some areas to the central government. In the United States, the federal government and its representatives are chosen by the democratic process of voting. This is not necessarily true in all Federal Republics.
The American system of government is a blend. It incorporates elements of a democracy: there is mass suffrage on some issues. However, it also incorporates elements of a constitutional republic. Officials must govern (ideally) according to limits established by a previously existing legal structure (the Constitution).
Nearly every country in the world is ruled by a system that combines 2 or more types of government. For example, the USA is not a true capitalist society, Our government does provides some services for its citizens. Additionally, one person's opinion of the type of government may differ from other people’s opinions. Many people argue that the USA is actually a plutocracy rather than a democracy.
In truth the USA is a Democratic Republic. A republic is led by representatives of the voters. Each is individually chosen for a set period of time.
This is true, our government is not truly a democracy (if of course you are referring to a direct democracy) because we elect representatives. This makes our form of government a representative democracy, better known as a Republic, because we elect educated and intelligent figures to make informed political decisions for the masses (regarded by John Locke as misinformed, unintelligent, and act out of passion rather than wisdom). However, we have saved some aspects of direct democracy, these are initiatives, recalls, and referendums. Initiatives and referendums are prospective laws written on voting tickets that citizens vote on. Recalls, are when voters vote, by a majority, to reelect a certain political official (the governor of California was recalled and replaced by Arnold Schwarzeneggar).