Studies of the fighting in WWII determined that most of the infantry fighting took place at distances under 200 yards, and those figures have not changed much in modern conflicts.(1) This was a revelation at the time and a controversial one, as ever since the development of smokeless powder, the long distance capabilities of military rifles had been stressed. It was common for rifles designed in the 1890s through the 1940s to have sights adjustable out to 1,000 or even 2,000 yards, and often not having an adjustment below 200 or 300 yards. Obviously, there was a discrepancy between the design of these rifles and how they were most often used.
Following WWII, the US military decided it needed a select-fire, detachable-magazine rifle. (The WWII-era M1 Garand had originally been designed with a detachable magazine, but at the time, the military decided they were a liability for a standard, front-line infantry rifle and had the M1 redesigned.) During this period during the late 40s and early 50s, many nations were experimenting with smaller-caliber rifles that were controllable in full-auto and allowed more rounds to be carried. The US military insisted on a 30 caliber rifle, though, and merely shortened the existing .30-06 Springfield (7.62x63mm) round to create the 7.62×51mm round, which Winchester released commercially as the .308 Winchester. The US also forced this round onto the newly-formed NATO, over protests that it was too much cartridge, would require rifles to be too heavy, and wouldn't be controllable on full auto. The first point is arguable, but the last two were certainly true. Still, the US military, having determined that the Belgium-designed FN FAL was a better rifle then the domestic M14 (a modified M1 Garand), chose the M14 anyway. Such is politics.
The M14 program was a political minefield and during the early 1960s, minor US involvement as "advisors" in the southeast Asian country called Vietnam was beginning to escalate. It didn't take long before the Vietnam expansion, coupled with manufacturing problems with some M14 contractors, resulted in too many soldiers and too few M14s. The military initially pulled WWII M1 Garands out of storage and pressed them back into service, but these long, heavy rifles were poorly suited to the jungle environment of Vietnam. During this time, Eugene Stoner of ArmaLite, the armament division of Fairchild Aircraft, had designed a rifle called the ArmaLite Model 10, or AR-10, which was chambered in the current NATO round of 7.62×51mm. Though the AR-10 was produced too late to enter the M14 competition, ArmaLite hoped to sell the AR-10 to foreign militaries.
Meanwhile, there was a faction of the US Military and the Congress which supported the idea of a lightweight, select-fire rifle firing a mid-power, small-caliber, high-velocity (SCHV) cartridge. After seeing the ArmaLite AR-10, they discussed their desire for a scaled-down model. ArmaLite engineers Jim Sullivan and Bob Fremont scaled down the AR-10 to fit the hot varmint cartridge of the day, the .222 Remington. During some preliminary military testing, it was decided that the .222 Rem wasn't quite powerful enough. Though the .222 Remington Magnum existed and had the power they were looking for, the severe shoulder angle would have prevented positive feeding in a semi-auto, and so it was decided that the best solution was to lengthen the .222 Rem case. The result was the 5.56×45mm cartridge, designed by G. A. Gustafson, which Remington released commercially as the .223 Remington. This cartridge has virtually identical ballistics as the .222 Mag and, over time, the wide availability of .223 guns and ammo has lead to the demise of the .222 and .222 Mag cartridges.
The AR15 was initially adopted by the Air Force, but the need for rifles for soldiers heading to Vietnam gave the "medium-power cartridge" supporters an opening and the AR15 rifle was hastily procured, initially as a one-time purchase. Continued problems with the M14 program lead to the official adoption of the AR15, which was given the US military designation "M16."
The national average engagement range for police 'snipers' has, for the past 20 years, been 78 yards. The FBI Hostage Rescue Team (HRT) snipers are limited to engagement ranges of 200 yards. The longest recorded shot taken by a police marksman in the US is 97 yards. (There are some reports that indicate some longer shots, including one alleged 300 yard shot in 1982 by the U.S. Park Police in response to a bombing threat at the Washington Monument- but these are very rare and not confirmed). The FBI's uniform crime report indicates that the average engagement range in a handgun incident is between 7 and 10 feet.