Berets of the United States Army
U.S. Army Special Forces wear the green beret because of their link to the British Commandos of World War II. The first Ranger unit, commonly known as Darby's Rangers, was formed in Northern Ireland during the summer of 1942. On completion of training at the Commando Training Depot at Achnacarry Castle in Scotland, those Rangers had the right to wear the British Commando green beret, but it was not part of the regulation uniform at the time and was disallowed by the U.S. Army. 
The 10th Special Forces Group (Airborne) had many veterans of World War II and Korea in its ranks when it was formed in 1952. Members of the 10th SFG began to unofficially wear a variety of berets while training, some favoring the red or maroon airborne beret, the black beret, or the green commando beret. In 1953, a beret whose design was based on that of the Canadian Army pattern, and which was rifle-green in color, was chosen for wear by Special Forces units.
Black beret
The black beret is a type of headgear. It is commonly worn by paramilitaries and militaries around the world, particularly armored forces such as the British Army's Royal Tank Regiment (RTR), the Royal Canadian Armoured Corps (RCAC), and the Royal Australian Armoured Corps (RAAC). Notable non-armored military units to wear the black beret include the Russian Naval Infantry (and formerly Soviet) and Russian OMON units, the United States Air Force (USAF) Tactical Air Control Party (TACP), Philippine National Police-Special Action Force (PNP-SAF) members, and the Royal Canadian Navy ("navy blue"). It was also worn by the United Kingdom's Royal Observer Corps (ROC) with their Royal Air Force (RAF) uniform, Metropolitan Manila Development Authority (MMDA).
Black berets are also worn by navies. In some navies, the naval color called black is officially "very dark blue". The Dutch Navy and Marines wear dark navy blue berets; a silver anchor for the Navy and a gold or dark brown (field duty) anchor on a red background for the Marines. The Portuguese Marines and San Marco Regiment, the Marines of the Italian Navy also wear a dark blue beret. The Royal Norwegian Air Force also use a dark blue beret. Finnish Marine Infantry wear a dark blue beret with the Navy insignia.(Finnish Coastal Jaegers - marine commandos - part of the same Nylands Brigade, wear the green beret).