I would argue that the novel is more relevant to modern readers now than it might have been 20 years ago. Right before the current recession, many Americans were living beyond their means. While they didn't live in Gatsby-esque houses, they were certainly buying houses and other material items that they could not afford to maintain. If one considers that the Roaring 20s led to the Great Depression (in part) and that America's obsession with materialism and propensity for taking on debt led to our current situation, then the modern reader should see many similarities between Gatsby's time period and ours.
Additionally, wealth is just as powerful in today's society as it ever was. In regards to the wealthy buying their way out of trouble or buying their way into positions of power, examples in politics and entertainment abound. Many of the powerfully rich still have an elitist attitude similar to the Old Money folks in Gatsby.
While our version of decadence might differ from Gatsby's and Tom and Daisy's, we still have shows such as Cribs, The Hills, The Real Housewives series, etc., that show the rich eating out every meal, paying exorbitant amounts of money for items of clothing, and furnishing their second or third homes as if it's nothing.
I would say yes and no.
I would say it is not relevant because very few people today experience the kind of decadent life that so many people in the book are living. There are some, and we see them on TV, but we don't live that life. (Of course, neither did most people when this book was written.)
However, I think you can argue that the idea behind the novel is just as relevant now as it ever was. I think that the book is largely about greed and materialism. I think that many people today who are not as rich as Gatsby are obsessed with getting material goods. I think people think they can buy their way to happiness just as Gatsby did.