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.
Israel Defense Forces insignia
Each corps in the Israel Defense Forces has a beret of a different color and/or a different beret pin worn by its soldiers, independent of rank and position. Israel Defense Forces soldiers wear berets on their heads only on formal occasions, such as ceremonies and roll calls. The beret is placed beneath the left shoulder strap while wearing the service uniform (alef), but not while wearing the combat/work (bet) uniform in the field. On base it is left to the unit's discretion whether to wear berets or field hats. Air force and navy officers, military orchestra soldiers and military police law enforcement soldiers wear combination caps. Formerly, male soldiers of all ranks wore combination caps, while female soldiers wore the garrison cap. In the 1950s, the beret was adopted as the default headgear for the service uniform. The color of the air force beret was blue-gray; armored corps, artillery, and special operations personnel wore a black beret. Paratroopers, following the pattern of the British Army, wore maroon, all other infantry wore olive drab. Combat engineers wore a gray beret. For all other army personnel, except combat units, the beret for men was green and for women, black. Women in the navy wore a black beret with gold insignia while men wore the traditional white sailor cap like that of the US Navy.