USS Enterprise (NCC-1701)
The original Enterprise is the ship that, along with its famous five-year mission, began the behemoth that is the Star Trek franchise.
The ship's first captain of note was Captain Christopher Pike. The ship gained its fame and prestige while under the command of Captain James T. Kirk. During the course of Kirk's five-year mission, the ship showed amazing resilience, and this was owed much to the well balanced and competent crew that served under Kirk, including Spock, Leonard McCoy, Montgomery Scott, Hikaru Sulu, Uhura, and Pavel Chekov.
After the five-year mission, Kirk was promoted to admiral and the position of captain was given to Matthew Decker. During this time, the ship was heavily refitted and upgraded, almost making it a whole new ship. As the refit was just being finalized, an unexpected threat from an unknown object approaching Earth gave Kirk the excuse to have himself declared captain of the Enterprise during the crisis, which he masterfully dealt with.
After the V'Ger incident, the Enterprise was transferred to Star Fleet Academy under the command of now-Captain Spock. While the ship was going on a training cruise, there was a problem with the Genesis Project that forced Kirk to assume command of the Enterprise in order to investigate the matter; since Kirk was one of the Star Fleet officers in charge of the project, he was the best to look into the matter. Unfortunately for Kirk, Khan had escaped his exile on Seti-Alpha 5 by hijacking the starship USS Reliant. Khan used his new ship to ambush Kirk on his way to space station Regula-One. In the ambush, he managed to heavily damage the Enterprise, but Kirk -- using his knowledge of Star Fleet procedures -- managed to force Khan to temporarily retreat. In a battle in the Mutara Nebula, Kirk and the crew of the Enterprise managed to defeat Khan and escape his detonation of the Genesis torpedo, but it came at the cost of the death of Spock.
After returning to Earth, the crew of the Enterprise found their ship was now slated to be scrapped. Soon, events lead to Kirk deciding to hijack the Enterprise in order to return to Genesis to retrieve Spock's body in order to complete his burial properly. Due to some side effect of the Genesis device, they found the living body of Spock on the planet. Unfortunately, in order to defeat a Klingon attempting to steal the secrets of Project Genesis, Kirk was forced to use the ship's self-destruct in order to give him a chance to capture the Klingon Bird of Prey, which he used to escape the disintegrating planet.