Question: I've read various pieces arguing that the USA is not a democracy, but a (fill in the blank, ex., a Republic). Perhaps there is no perfect fit, but **which form of government does the USA most closely match?**

Answer: 
The United States is a **[Representational Democracy](http://en.wikipedia.org/wiki/Representative_democracy)**. The people have no direct say in government, but have the ability to freely vote for those who *do* have direct say (the people's representatives).

This is contrast to a Direct Democracy (which is also sometimes called just a "Democracy" or a "pure democracy"), where every citizen is entitled to a vote on every issue (such as ancient Athens), and a Delegate Democracy where citizens may temporarily give their votes to a chosen delegate who can vote them as a bloc (similar to a corporate board). There are [other types of democracy](http://en.wikipedia.org/wiki/Types_of_democracy) it's also not.

It is also a Republic, which is a term that can be applied to any country which is democratic but not a direct democracy. Technically, this makes the US a [Democratic Republic](http://en.wikipedia.org/wiki/Democratic_republic), but the countries which currently use that term do *not* use it in that way, and that usage isn't common.
You cannot counter-posite democracy to a republic. Republic is a well-defined form of state. As such, the US is republic. Democracy is a form of government. There can be various degree of democracy and various opinions on what practice is more democratic.