The United States is largely capitalist, but with many socialist
programs. Just to name a few - Medicare, medicaid, social security,
welfare, public schools, public roads, soon (knock on wood) semi-public
health care, and pretty much any other program run by the government.
A purely capitalistic state would presumably involve multiple
corporations in competition acting as their own pseudo-government,
taxes would be replaced by optional payments to these corporation in
exchange for protection by the corporation. This protection would be
carried out by an armed force paid by the corporation. Those who didn't
pay would not be protected, enabling people to do things to them that
they could not do to those who did pay for protection.
Chances are, conflicts would break out between these corporations at
some point, and the corporations would use their armed forces to force
those who opted out of the protection fees to pay them, rendering these
payments no longer optional. Eventually, each of these corporations
would stake out their own land in which everyone would be forced to pay
protection to the corporation.
If you think about it along these lines, the United States government
is nothing more than a democratically elected corporation that forces
everybody to buy protection under the law. However, I'm not in any way
saying that this is a bad thing, as the government also provides the
above socialist programs along with enough capitalism to entitle the
individual to (most of) the fruits of his or her labor.
In other news, I just pulled a possible explanation for the political history of the world out of my ass.