U.S.S. Enterprise (NCC-1701)

Launched in 2245, the original and illustrious starship U.S.S. Enterprise NCC-1701 was built in the San Francisco Yards orbiting Earth. The Constitution-class starship was previously captained by Robert April and Christopher Pike, before coming under the command of Captain James T. Kirk. 
The ship arguably gained its status as the most famous space-exploration vessel in history due to its historic five-year mission from 2264-2269. During this mission, Enterprise encounted the Romulans for the first time since the Romulan-Earth conflict, engaged the robotic "Planet Killer" vessel, traveled back in time to 20th-Century Earth, and played host to Khan Noonien Singh, a product of late-20th Century genetic engineering who once fought in the Eugenics Wars. 
Kirk's Enterprise had a crew of 430, 14 science labs, an observation deck, a massive lower deck which included main engineering, and a shuttle bay. The ship's armaments included forward phaser banks and photon torpedoes.
The starship underwent several refits, most notably in 2270, which involved an upgrade of most systems and the replacement of the bridge and warp-drive nacelles. This refit Enterprise was, first, commanded by Captain Williard Decker until the V'Ger incident forced a then-Admiral Kirk to assume command. 
In 2285, Admiral Kirk assumed command from Captain Spock during a training mission when the Enterprise was diverted to investigate Regula 1. Ultimately, this divergence would result in Kirk's second encounter with Khan, and a brutal combat between Enterprise and the ship Khan hijacked, the Reliant. Captain Spock died on this mission. 
Shortly before its decommissioning in 2285, Kirk took the Enterprise -- against orders -- to the Genesis Planet to rescue a rejuvinated Spock. It was also here that the vessel was destroyed by Kirk when threatened by Klingon capture.