Jay Gatsby's dream was the quintessential American dream - success (money and riches) through whatever means one deems necessary. In this case, Gatsby began a penniless but determined to make his life better than that of his parents:
"His parents were shiftless and unsuccessful farm people - his imagination had never really accepted them as his parents at all. The truth was that Jay Gatsby, of West Egg, Long Island, sprang from his Platonic conception of himself" (104).
To him, his parents were unsuccessful and surely they could not really be his parents when he was destined or greater things. Through bootlegging, Gatsby made his riches. He became well-known and people came to his house every weekend for huge elaborate parties.
But, Gatsby's downfall was this exact same thing - success through whatever means one deems necessary. He did not honestly earn the money, and he spent his life trying to cover up lies and make himself seem great. Daisy was the one part of his American dream that he did not yet have, but fter Tom and Gatsby have their great argument in the city, Gatsby is sure he has just snagged her. However, Gatsby's penchant to lie about everything is his ultimate downfall. He lies about who was driving the car, which means that Tom is willing to tell Wilson that the car belongs to Gatsby. And just like that, Daisy escapes without punishment - and she still has a man - but Gatsby has lost everything.
After his death, we see the downfall and destruction of his American dream. His unsavory work-friends refuse to get 'mixed-up' in his death. The people who came to his parties were people that he did not actually know and they did not come to the funeral. Tom and Daisy left town after it happened, so the girl Gatsby wanted did not even come to the funeral. The only person who did come was Gatsby's father, a man whom Gatsby despaired of because he was poor and nonrepresentational of the American Dream.
Dishonesty is the downfall of Gatsby's American Dream, as it is the destruction of everyone else's - except Nick's - dreams as well. After all, as Nick stated in chapter 3:
"I am one of the few honest people that I have ever known" (p. 64)
Gatsby’s dream was to win Daisy but was corrupted by money and dishonesty just as the American dream of happiness and individualism has disintegrated into the mere pursuit of wealth. Though Gatsby’s power to transform his dreams into reality is what makes him “great,” Nick reflects that the era of dreaming—both Gatsby’s dream and the American dream—is over.