I really don't think race is as important today as it once was. The fact is, if you're rich and black, you're going to do just fine. And if you're poor and white, you're going to face problems, just like your poorb black counterparts. So, I think people all of races from low-income backgrounds (re: possibly crummy schools, maybe unsupportive parents, etc.) should perhaps be granted some sort of slight advantage.
Let me also note that I've seen the American dream at work. My hometown has a huge (50%) Hispanic population, and most of my close friends from high school are either Mexican or Guatemelan. Their parents work full-time *hit jobs at either Wal-Mart or the local cow slaughterhouse. They speak absolutely no English. Yet given these unfavorable circumstances, their children are all attending four-year public schools and are well on their way into the middle class. How is that possible? Isn't there rampant modern racism and institutional discrimination? No, there isn't. Here's what the parents do. They live modestly. They don't do drugs. They are strong in their Catholic faith. They remain married and thereby pool two incomes. They pester their kids about the importance of education. They're not too proud to want better for their kids. And they work their tails off, because no welfare is available for illegal immigrants. I am not insinuating that other racial minorities are lazy scoundrels, but the American dream still exists. You just have to work at it.