The United States has historically been regarded as a country with an open social class system, high levels of mobility, and equal opportunity. Over the past two decades there is growing cross-national evidence that the U.S. is no longer the nation that allows for the greatest levels of mobility. In fact, there are many countries, particularly the Northern European countries, that consistently outperform the US in the ability of children to move into different income and class categories from their parents (intergenerational mobility).
The following graph provides one potential explanation for the lack of mobility in the United States -- growing income inequality. There is a strong positive correlation between income inequality and intergenerational immobility.
This is taken from Lane Kenworthy's excellent blog Consider The Evidence, which also includes links to various sites where these data are discussed and debated.