People like Piers Morgan continually make the point that we don't allow people to purchase tanks or 50 caliber machine guns to defend themselves from government tyranny, so why allow AR-15s. The answer? It is true that society has decided that people should not be able to arm themselves with an Abrams tank, or F-16. But, despite all the technological advances since the Constitution was written, society still believes the core idea of defense against potential tyranny applies. As noted by the ChineseTienanmen Square dissident, a mass number of armed citizens would indeed be able to turn back a modern army -- unless that army was prepared to level a whole city. (The quote is "The argument that a man with a rifle has no standing against the military technology and machine of today" is ridiculous. 20,000,000 residents of Beijing would have quickly proved that wrong had they been armed in 1989."
Essentially, the argument for allowing citizens AR-15s is the concept first advanced by France with its Force de Frappe or Force de dissuasion./ A brief history lesson is in order regarding this, as it is directly applicable to the question Piers Morgan just doesn't get. In sum, after Charles de Gaulle's return to power in 1958, he was concerned that the US would not protect France from a Soviet invasion -- by the 1960s, the US was knee deep in Vietnam, and besides, why would the US risk America for France? As Wikipedia notes -- and is critical to the discussion here -- "The strategic concept behind the Force de Frappe is one of countervalue, i.e., the capability of inflicting to a more powerful enemy more damage than the complete destruction of the French population would represent. The enemy, having more to lose, would therefore refrain from proceeding any further. This principle is usually referred to in the French political debate as dissuasion du faible au fort (Weak-to-strong deterrence) and was summarized in a statement attributed to President de Gaulle himself:
"Within ten years, we shall have the means to kill 80 million Russians. I truly believe that one does not light-heartedly attack people who are able to kill 80 million Russians, even if one can kill 800 million French, that is if there were 800 million French." Similarly, General Pierre Marie Gallois said "Making the most pessimistic assumptions, the French nuclear bombers could destroy ten Russian cities; and France is not a prize worthy of ten Russian cities" and French Admiral de Joybert in his book La paix nucléaire (1975), simply put it this way "Sir, I have no quarrel with you, but I warn you in advance and with all possible clarity that if you invade me, I shall answer at the only credible level for my scale, which is the nuclear level. Whatever your defenses, you shan't prevent at least some of my missiles from reaching your home and cause the devastation that you know. So, renounce your endeavour and let us stay good friends."
The above, along with the facts that the AR-15 has indeed been used multiple times for home defense (as noted in this attached paper), and is almost never utilized in crimes, is the answer why we should allow so called "assault rifles" to the public.
NOTE: Updated (1/30/13) PDF file now available here.