The American dream was an ideal of the United States of America. It essentially encompassed "truth, justice and the American way". (TLG: "Pilot", et al.)
When John Fitzgerald Byers was a boy, the American dream was one topic that his father, Bertram Roosevelt Byers, used to talk about. The stories inspired John Byers to believe in the promise of his country. In 1989, he teamed up with Richard Langly and Melvin Frohike, an action that he later claimed was due to his belief that "someone has to expose those who would destroy that dream, someone has to write the stories they don't want you to read." (TLG: "Pilot")
Ten years later, FBI Special Agents Fox Mulder and Dana Scully conducted an undercover investigation of the Falls at Arcadia planned community and dined, one night, with fellow residents Win and Cami Shroeder. When Mulder implied that he believed the Falls at Arcadia (like other communities) had a dark underbelly, Win Shroeder defended the planned community by saying that it was, as far as he was concerned, the American dream. His wife, Cami, then took their dog, Scruffy, for a walk and was joined by Scully, who asked Cami for her thoughts on whether the area was the American dream. Rather than directly answering the question, Cami admitted that the place was a "nice neighborhood", made up of people who wanted the best for their families. (TXF: "Arcadia")
When John and Bertram Byers were temporarily reunited in 2000 - after having become estranged in 1989, because Bert Byers had disapproved of his son associating himself with Langly and Frohike - Bert Byers' final words to John were an acknowledgment that he and his friends were fighting for the American dream (an indirect reference to The Lone Gunmen's newspaper, The Lone Gunman) and a caring caution that he should not expect to win. (TLG: "Pilot")
In 2002, moments after Scully discovered that a particular man had been spying on her, she spoke to the man - unaware at this time, however, that he was a super-soldier - and asked him if he had ever heard of the Constitution. Her observer answered that he had, before saying that it "allows foreign terrorists to live here and enjoy the American dream, until time comes to destroy it." (TXF: "Trust No 1")