J. Edgar Hoover Building
Headquarters of the FBI in Washington, D.C., and consequently home of the intrepid duo Mulder and Scully. The building takes its name from the FBI's original director, who is credited with making the initials FBI a potent symbol of US law enforcement. Since The X-Files' second season Simon Fraser University has stood in for the real J. Edgar Hoover Building, with the identifying signs replaced with J. Edgar copies made by the props department. Don't believe everything you see on TV. 
JFK
According to The Lone Gunmen's rather subjective investigations into Cancerman's life, this was the first thing said by Mulder, at the time one year old. Mulder's father cheerily told a young Cancerman this when they were both stationed at the Center For Special Warfare in North Carolina. Cancerman neatly followed this with the rather extreme tit-for-tat gesture of personally shooting JFK in the same episode, Musings of a Cigarette-Smoking Man. 
Jersey Devil
The mythical beast which allegedly attacks people in and around the New Jersey Woods. When Mulder finally meets her face to face, he describes her as "beautiful," yet earlier Scully dismisses the stories as folk tales. Meanwhile, as Mulder puts forward his case that the creature is merely defending itself, Scully comments "This thing chewed somebody's arm off! That's not exactly a defensive posture!" This episode, Jersey Devil, is also significant because (get this!) Scully has a social life! She's just in the middle of a romantic meal with Rod when Mulder rudely interrupts - shame that, they were just about to discuss the nitty gritty of state planning and taxation.