In historical context, the militia included in the 2nd Amendment was not only the "standing militia" like the National Guard. Every man would be allowed to own and train with firearms so that, if necessary, they could be called up to form the militia on an ad hoc basis to respond to emergencies. They were required to provide their own weapons (hence the need to own firearms and other weapons, rather than them being provided for them).

Federalist Paper Number 29 goes into further detail regarding their motivations and attitude of the drafters of the Constitution and Bill of Rights behind the Second Amendment.

Historically, the unorganized militia is a descendant in spirit, if not in exact historical progression, from the Anglo Saxon Fyrd, which was the body of free men able to be called up to defend the shire when necessary.

You may have not heard many politicians or journalists talk about it, but this distinction is at the heart of the right to keep and bear arms. There have been efforts made to define the militia SOLELY as the National Guard (the organized militia), obviating the need for an unorganized militia of armed citizens. Obviously, politically this has not been feasible.

The Militia Act of 1903 defines the unorganized militia as all able-bodied males between the ages of 18 and 45.

United States vs. Miller, a Supreme Court case in 1939, held that sawed off shotguns could constitutionally be regulated as they were not appropriately weapons used by the militia/military at the time (though they are now). In that case, however, the respondents and their attorneys did not show up for court, so the court essentially had to accept the government's argument at face value.

The Supreme Court has since held in District of Columbia v. Heller that the Second Amendment protects a person's right to possess firearms for traditionally legal purposes. (This might run afoul of the 20 year rule here, but I felt a quick mention is necessary to give a balanced view of current jurisprudence).

Further Reading: The Samurai, The Mounty and the Cowboy is an excellent discussion of the cultural and historical reasoning behind the American emphasis on individual freedom vis a vis weapons in contrast to other states.