Star Trek is a franchise of several science fiction television series, and feature-length films.
Assistant Director Walter Skinner told Wayne Federman that Fox Mulder investigated cases in a "Star Trekky" way, which is part of the reason why he used Mulder's likeness for his movie. (TXF: "Hollywood A.D.")
There have also been several references which allude to Star Trek, without mentioning it by name.
In TXF: "Dreamland" and "Dreamland II," there are two more implied references to Star Trek. In part I, Jeff Smoodge mentions the phrase "Beam me up, Scotty". In part II, a home movie reel is shown, with a young Fox Mulder dressed as Mr. Spock, a popular character from Star Trek.
In the first X-files time travel episode Mulder and Scully show a composite sketch to Lisa Ianelli that bears an uncanny resemblance to Captain Picard instead of the villain. Several minutes later a victims flight number is shown as Pan Oceanic Flight # 1701. (TXF: "Synchrony")
The scene in "Jump the Shark" in which the Lone Gunmen die pays homage to a scene in the movie Star Trek II: The Wrath of Khan. In that film, the character of Spock saves the U.S.S. Enterprise, but has to sacrifice himself by being sealed in a radiation chamber to do so. Before his eventual death however, he is able to talk to his commanding officer and friend, Captain Kirk, through a wall of glass. The Gunmen make a similar sacrifice, by sealing themselves in with an airborne virus in an airtight fire door. They are also able to speak with Jimmy Bond and Yves Adele Harlow through a pane of glass shortly before they die.
In the DVD audio commentary for "Je Souhaite", Vince Gilligan recalls that, in his original concept for that episode's story of someone finding an android in a long-locked-up self-storage locker, he had thought the idea of incorporating an android seemed more to him like Star Trek than The X-Files.
- Star Trek (Memory Alpha)