Though statistics suggest that financial/economic mobility in the US is on the decline, the quintessential American Dream seems to remain intact. Americans believe in the principals of the equalizing force of work, in the right to self-improvement and economic self-definition.
Despite his tragic ending, Gatsby lived the American Dream. He decided early on that he wanted more than his poor life could afford him, and he achieved success in all kinds of areas. He even had a shot at the girl. Unfortunately, he chose someone who had become shallow and self-absorbed and she did not remain true to him; however, he did win her, at least temporarily, twice in his short life. He had a chance, and that's the American Dream, both then and now.
The American Dream is ultimately about opportunity and freedom to choose the life you want and the chance to make something of yourself no matter where you come from. In that sense, Gatsby rises from his modest beginnings and achieves the wealth and success he had wanted since childhood. He has the chance to achieve personal happiness, but while the results are not what he would have liked, he at least had the chance.
For Gatsby and for others in the 1920s, wealth was a means to possibly rise in society, at least in part. Jay Gatsby does have the New York socialites at his parties, and his house is near where the elite live. Nowadays, the wealthy do not wish to associated with the socially prominent as much as they prefer celebrities, who are themselves from all social classes.
For others, the American dream is about coming from a third-world country to the United States where they can be "taken care of" through various welfare programs.
I would argue that Fitzgerald's portrayal of the American Dream in this book is a biased one. He is looking critically at the society he lives in, seeing only the materialistic people like the ones he portrays in the book. You could certainly say that such people still exist today. All you have to look at is something like MTV Cribs to see that there are people for whom the American Dream is nothing but material wealth.
However, both in the '20s and today, there were millions of Americans whose dream did not resemble that of the book. There were and are so many people who see personal fulfillment and spiritual and intellectual growth as their major goals. These people get lost in the stereotypical views of the "Roaring '20s" or of today's materialism, but I would argue that they outnumber the shallow materialistic people.
So, I would say that the American Dream has not changed. But I would also argue that it is not really the way that Fitzgerald portrayed it. The American Dream was and still is about more than shallow materialism.
I think that you are probably going to get a great deal of discussion on this point. Gatsby's initial pursuit of his dream is one that is motivated and driven by material wealth. I think that in this regard the American Dream is still present. Money and materialism is still a part of the American Dream. I think that the manner in which Fitzgerald depicts this pursuit as one- dimensional might have changed a bit. Gatsby zealously believes that the more money one has, the greater the chance their dreams are going to be fulfilled. While we see many elements of this in the modern setting, I think that there is a greater acceptance that monetary success is not the sole factor in determining the American Dream. There are other elements that are acknowledged in the completion of this dream. Money and materialism are both still present, and there are significant people who still see their pursuits in the same light as Gatsby's. However, I do believe that more people are willing to concede that the definition of the "American Dream" envelops more complexity than Gatsby would have believed. If nothing else, Gatsby's failure and others in both literature and real life have brought a level of intricacy where individuals have to concede that money is not the sole determinant for their dreams' fulfillment or happiness.