Captain America's Motorcycle is Captain Steve Rogers' personal motorcycle. The original was a World War II era motorcycle modified for Rogers' personal use in combat on the battlefields of Europe. After being frozen and revived in the modern age, Captain Rogers continued using modern model Harley-Davidsons for both personal use and during active missions as an agent of S.H.I.E.L.D. and as a member of the Avengers.
World War II Era
Captain America's Motorcycle was a 1942 Harley-Davidson WLA "Liberator" with custom additions made for the personal use of Captain Steve Rogers during his service in World War II. It began as a standard Harley-Davidson model motorcycle that was modified by Howard Stark and the Strategic Scientific Reserve, who added several weapons and gadgets for use in combat situations.
Near the end of the war, in a plan to infiltrate HYDRA Headquarters, Captain America used this motorcycle to attack the base head-on, as well as serving as a distraction for the Howling Commandos and other SSR forces to break in. The bike's gadgets proved useful in taking out a squadron of HYDRA soldiers on motorcycles patrolling the outside of the base. As Rogers approached the base, he used the motorcycle to jump the main wall. He abandoned the bike after setting it to self destruct, aiming the bike for the base's main blast doors, which were taken out by the resulting explosion.
Decades later, a replica of Captain America's World War II era motorcycle was put on display at the Smithsonian Institution in Washington, D.C., alongside other displays documenting the activities of Captain America, the Howling Commandos, and the Strategic Scientific Reserve during World War II. 
During the Chitauri Invasion, Captain Rogers relied on a 2012 Harley-Davidson Softail Slim as his personal form of transportation. However, due to changes in modern forms of transportation and the variety of his new assignments under S.H.I.E.L.D., he rarely, if ever, used his motorcycle while running missions and regulated it to personal use only. When regathering with the Avengers following the Battle of New York to see off Thor, Loki, and the Tesseract on their return to Asgard, Captain America arrived and departed on his motorcycle.
During the HYDRA Uprising, between running missions for S.H.I.E.L.D., Rogers drove a 2014 Harley-Davidson Softail Breakout as his personal motorcycle. After Captain America was branded an enemy and fugitive by Alexander Pierce, he attempted to escape from the Triskelion on a 2014 Harley-Davidson Street 750. Rogers was able to expertly maneuver past roadblocks and other security measures, even engaging a Quinjet head-on as it opened fire upon him.
During the War on HYDRA, Rogers once again drove a Harley-Davidson Street 750 (the same model motorcycle he drove during the HYDRA Uprising) during the Attack on the HYDRA Research Base in Sokovia before he performed a somersault and threw it at a Humvee filled with HYDRA soldiers. 
1942 Harley-Davidson WLA "Liberator"
Captain America's Motorcycle had the same capabilities as a Harley-Davidson model motorcycle of that era, along with the added capabilities granted by the gadgets and upgrades added by SSR engineers. Enhancements included a deployable trip wire and a rear-facing flamethrower to eliminate pursuers, twin mini rocket launcher barrels mounted to the front of the bike, and a delayed self destruct function, all controlled from a control box on the right handlebar. Additionally, Rogers could fix his shield to the front of the bike to block and deflect on-coming fire from HYDRA weapons.