In Star Trek IV, the "part" of USS Enterprise was actually filled by the conventionally-powered USS Ranger (CV-61, Forrestal-class), because Enterprise was on deployment at the time of the movie's filming. (Star Trek Encyclopedia 2nd ed., p. 137) At the time of the filming, the reactor arrangement of all American nuclear aircraft carriers was tightly classified. Ranger also stood in for Enterprise in the 1986 aviation thriller Top Gun. Ranger differed from Enterprise in the shape of the ship's command "island" superstructure (which was longer, rectangular and possessed smokestacks for the ship's oil-fired boilers) and the placement of the side elevators, with two abaft of the island instead of two before it. Both differences were visible in Star Trek IV.
In the real world, Enterprise was nicknamed "the Starship," after her fictional namesake. She was in commission from 1961 to 2012.
In April 1983, the Enterprise, half a mile from shore after a 14-month, 46,000-mile cruise, ran aground in San Francisco Bay; George Takei was aboard the ship during this incident. 
In 1993 and 1994, the Star Trek Association of Towson, a fan club in Towson, Maryland, sponsored "The Big E Con," a convention held aboard the carrier Enterprise while the ship was at its home port of Norfolk, Virginia. The events featured tours of the ship and appearances by Star Trek notables. The fan club also donated Star Trek memorabilia for display in the ship's recreation room.
In the novel Debtors' Planet, this Enterprise was a casualty of the Eugenics Wars, lost with all hands in the Sea of Japan in 1995 during the pivotal battle of the wars (the book was published in 1994, seven years before Greg Cox' novel trilogy retconned them as a collection of shadow conflicts rather than open warfare), from which Khan and his forces never recovered. Ralph Offenhouse's son Peter was one of the sailors killed in the sinking - ironically, in Cox' works, his father was an early financial backer of the Chrysalis Project, from which the Augments were created.