I absolutely find the major themes and attitudes of the book to be relevant today, almost a hundred years after its publication. Fitzgerald conveys the idea that the American Dream—the notion that someone can come from nothing and, through hard work and diligence and perseverance, achieve wealth and success—is a fantasy. No one in the text can actually achieve it: not the hardworking George Wilson (who is duped again and again by Tom Buchanan, upper-class racist and all-around jerk); not the perhaps likable but ultimately criminal Jay Gatsby (you aren't really living the dream if you obtain your wealth through illegal channels); not Tom or Daisy Buchanan or Jordan Baker (who aren't on a quest to achieve the Dream, anyway, because they are already wealthy and successful as a result of their old money inheritances); not even Nick (who becomes so disillusioned with Wall Street, New York, and the upper class that the only thing he obtains is cynicism).
The American Dream can, likewise, be seen as a fantasy today. It is very rare to actually learn of a person who "came from nothing" and achieved great wealth and success. There are people who work three or four part-time jobs, hoping to cobble together something like a living wage with which to support themselves and their families; they can work hard and be diligent, but they might never even obtain health insurance, let alone "wealth and success." There are programs, of course, meant to help individuals with fewer resources, but even those programs are threatened and constantly under fire, especially now. There is still 1–2% of the population in America that possesses 90+% of the wealth in the country, and the other 98% of the population will simply never achieve anything approaching that kind of money. Even the middle class, the group once thought to have achieved the dream, is disappearing as the gap between the "haves" and the "have nots" grows wider and deeper. Yes, the subjects Fitzgerald tackles remain incredibly relevant still.