You are the great western light of California, torchbearers in the darkness, living reminders of all that is best in our republic.”— President Kimball
The origins of the NCR's army are not detailed, however, by 2241 it was the largest standing force in New California composed of several divisions.
Some amount of time after the Destruction of Control Station ENCLAVE, an early major engagement of the NCR's army took place during the NCR-Enclave conflict, where the NCR, alongside the Brotherhood of Steel, overran and annihilated the Enclave's last known holding in New California.
While the casualties on the NCR's side were tremendous, the Brotherhood of Steel finished off the remaining Enclave soldiers stationed there, with only a few managing to escape into the wastes. 
The NCR's army has continued to grow and serve NCR's interests, securing its expansion and protecting territories under its control. It has distinguished itself both in its near destruction of various raider tribes such as the Vipers, the Jackals, and the Khans, and proved quite resilient in the war against the Brotherhood of Steel.
By 2281 they were the largest armed forces in the entire Mojave Wasteland, rivaled only by Caesar's Legion, who were gathering their forces for another attack on Hoover Dam.  The Republic protected Hoover Dam and other outlying territories falling under the limited jurisdiction they possess in the Mojave Wasteland, though the stalemate with the Legion forced them to stretch their forces far and thin along the Colorado River.
Troopers are volunteer and conscripted forces in the NCR's military. They vary widely in devotion, experience, and even in basic equipment. What they lack in consistency they make up for in numbers.”— Fallout: New Vegas loading screen
The military's organization is inspired by the pre-War American structure, although adapted to the much smaller population of the wastelands. The standard level of organization of infantry forces is the battalion, which in turn is divided into companies under the command of a Captain. Companies are in turn divided up into platoons, for example Lieutenant Hayes in Primm is in charge of a platoon which belong to the 1st Company, 5th Battalion. These are sometimes divided into squads (created at the Commanding Officer's discretion) and are typically led by a sergeant or other non-commissioned officer, for example Sergeant Lee, who commands the strike force sent to retake the NCR Correctional Facility from the Powder Gangers.
Other branches in the military separate from the regular army include NCR Recon (which includes 1st Recon), the NCR Heavy Infantry Corps which are under direct command of General Lee Oliver, medical corps, logistics corps (quartermasters are typically non-commissioned officers), and the NCR military police.
Military bases of the Army, typically called Camps, are always under the command of a commissioned officer (usually a major e.g. Polatli or Knight). The larger camps that train recruits, such as Camp McCarran, will also have Drill Sergeants.
Relations with the outside
The NCR's military doesn't like being in the role of "peace-keeper". Crimes across the Mojave are typically punished by death.”— Fallout: New Vegas loading screen
Matters of diplomacy are left to be decided by the civilian branch of the government, such as the President and the Congress, with the outsider view of the military generally depending on their relationship with the NCR.
Groups that are considered enemies of the NCR, such as Caesar's Legion, the Great Khans, Brotherhood of Steel, and the Fiends are all openly hostile towards NCR military personnel, and frequently clash in violent battles. Due to their mutual hatred for the NCR, Caesar's Legion sent an emissary to the Great Khans on the pretext of forming an alliance to fight them, by absorbing the Khans into the Legion. Some small bands of settlers and bandit groups are antagonistic towards the NCR army (and the NCR as a whole) because of feelings of unwanted imperialism or complaints of poor quality of governance.
The New California Republic's military is large and diverse, composed of various organizations, of which the largest and noticeable is the Army, the NCR's main armed ground forces.
The Army features a basic training regimen, consisting of a two-to-three week series of abbreviated tutelage on weapons familiarity and explosive ordnance handling, along with intense physical conditioning. The reason for this short training period is to produced field-ready troops as soon as possible, to meet the fitted needs for personnel size based on their mission, especially with the Mojave Occupation where there are high casualties and troops are killed daily.
The bulk of the army is composed of troopers, a mixture of trained volunteers and conscripts that are employed in offensive and defensive missions. Their large numbers mean the troopers utilize mass produced equipment made from durable materials that perform reliably and can survive harsh treatment. The basic primary weapon is a semi-automatic 5.56mm service rifle, but troopers can also be equipped with hunting rifles, or varmint rifles and caravan shotguns when there are shortages. The M&A 9mm pistol is the standard sidearm of all members of the NCR Army. All of these weapons are provided by the Gun Runners, who handle a majority of the weapons contracts of the army. Uniforms for troopers is standardized NCR armor, supplied by the Crimson Caravan Company. It consists of a reinforced leather breastplate on the torso and upper back, supported by leather shoulder-pads worn over brown fatigues. Despite the modest training and equipment the troopers receive, it is superior to equipment employed by most adversaries of the NCR, namely raiders, nomadic tribes or the numerous recruit legionaries of Caesar, who are rarely sent into battle wielding more than a mere machete or crude pistols.
Heavy Infantry Corps
The Heavy Infantry Corps are much better trained and equipped than the standard troopers, and while they are still technically part of the Army, they are under personal command of General Oliver. They are equipped with NCR salvaged power armor, suits of scavenged T-45d power armor with the servos and pistons removed, which the NCR gained from their war with the Brotherhood of Steel, giving them superior protection than the standard soldiers. They carry heavy weaponry, such as the high-capacity light machine guns, and occasionally missile launchers.
A separate special forces branch, known as the NCR Rangers, became a part of the NCR in 2271. The Desert Rangers signed the Ranger Unification Treaty with the NCR at the Mojave Outpost, in which they agreed to become part of the NCR military in exchange for protection of Hoover Dam and Nevada from Caesar's Legion. Most Rangers wear NCR-designed Ranger patrol armor, while veterans opt for the so-called Black armor: a traditional Desert Ranger trenchcoat worn together with a pre-War riot armor and helmet. Rangers have access to superior weapons, such as trail carbines, anti-materiel rifles, and brush guns.
The NCR has very limited airpower, possessing a small fleet of captured Vertibirds reserved for political VIP's, with at least one Vertibird named "Bear Force One" reserved as the president's personal vehicle.
The New California Republic has a mechanized vehicle division. However, the exact number and the type of vehicles in the division is unknown. The logistics corps employ several scavenged US Army trucks for transport. These are kept running by a dedicated team of mechanics and well-stocked workshops, such as the truck repair depot at Camp McCarran.
The NCR possess various pre-War weapons and equipment as well. Hoover Dam is protected by an anti-aircraft gun capable of firing flak shells to bring down aircraft. After the NCR gained control of the HELIOS One facility by forcefully taking it from the Brotherhood of Steel in Operation: Sunburst, they had unknowingly gained possession of the Archimedes I and Archimedes II super-weapons.
The New California Republic has gone to war several times. A chronological order of the wars they fought are as followed: