Star Trek is one of the most successful and well-known science fiction franchises of all time. Conceived by Gene Roddenberry in the mid-1960's, Star Trek has evolved into a massive canon franchise including five live-action television series, twelve movies, an animated series, video games, comics and hundreds of novels. Star Trek is renowned for its enormous and dedicated fan base. In 2009, the movie "Star Trek" came out using the original USS Enterprise crew and rebooting the film series using an alternate timeline. The reboot's sequel, Star Trek Into Darkness, was released 9th May 2013.
As science fiction nerds, Leonard, Sheldon, Howard and Raj are all fans of Star Trek. There have been references made to the first four television series - Star Trek: The Original Series, Star Trek: The Next Generation, Star Trek: Deep Space Nine and Star Trek: Voyager - the first six films, Star Trek: First Contact, and J.J. Abrams' 2009 reboot film, but none yet to the fifth and final television series Star Trek: Enterprise or directly to Star Trek: The Animated Series. Of all of the movie and television franchises that are referenced in the show, Star Trek is mentioned most often.
Both Leonard and Sheldon agree that The Original Series is better than The Next Generation, but that Captain Picard of The Next Generation is superior to Captain Kirk of The Original Series. Sheldon believes that Star Trek: The Motion Picture was the worst movie and Star Trek IV: The Voyage Home was “in-arguably the best,” while Raj believes Star Trek V: The Final Frontier to be the worst and Star Trek II: The Wrath of Khan to be the best.
References to Star Trek in The Big Bang Theory are frequent. All four male main characters are fluent in Klingon and often play Boggle in the language. Leonard has every day and dress Star-fleet uniforms, Sheldon has a Spock uniform, and Raj has an Uhura uniform that Priya wears. All of them can recite Spock's dying words, and Sheldon has recited dialogue of Khan Noonien Singh as well as Picard's speech about drawing the line in Star Trek: First Contact. Sheldon, a self-proclaimed honorary graduate of Starfleet Academy and Captain Kirk of theoretical physics, introduces "Rock-Paper-Scissors-Lizard-Spock", invented by Sam Kass, and the guys always choose Spock. Sheldon has an adversarial relationship with Star Trek: The Next Generation star Wil Wheaton, who has appeared as a fictionalized version of himself on four occasions. Sheldon likes Mr. Data but Brent Spiner replaces Wheaton as his enemy.
Sheldon invites LeVar Burton, TNG's Geordi La Forge, to his home for a raffle, but he comes too late for anyone to notice him. Meanwhile, George Takei has appeared to Howard in his mind. Leonard has mentioned the Romulan Neutral Zone. The constant references to Star Trek seem to have had some influence on Penny, who was shocked when she referenced deflector shielding to Alicia in The Dead Hooker Juxtaposition. She also mentioned that her shields were up below the waist when she spent the night in Sheldon's bed in The Love Car Displacement.
Spock appears as an in "The Transporter Malfunction" (S05E20). The action figure is voiced by Leonard Nimoy and talks to Sheldon in his dreams.
In "The Codpiece Topology", the guys return to the Renaissance Fair with Sheldon portraying a Vulcan Star Fleet officer (probably Spock) from a landing party observing a planet that resembled middle-ages Earth which also included strange modernistic anomalies.
In "The Thespian Catalyst", Sheldon is taking acting lessons from Penny and they are performing a short skit based upon a story Sheldon wrote as a child. Penny portrayed Mr. Spock.
Spock is the Star Trek character that Sheldon most identifies with since he feels they are both intelligent, logical and unemotional. Also, when Sheldon describes their group as a Star Trek landing party, he is Spock, Leonard is Kirk, Howard is Scotty and Raj is the guy in the red shirt that is killed or is Lt. Uhura.
After "The Colonization Application" and after "The Leftover Thermalization" preview, The Big Bang Theory gave tribute to Nimoy by Chuck Lorre's vanity card saying, "The Impact you had on our show and on our lives is everlasting". A similar tribute happened to Carol Ann Susi.