Snrrub, every time I have read comparative studies, the USA tends to have the highest income mobility. That means it is actually easier to "move up" in the USA than anywhere else.

Here is a recent article I read on the subject:

Movin' On Up

The Treasury study examined a huge sample of 96,700 income tax returns from 1996 and 2005 for Americans over the age of 25. The study tracks what happened to these tax filers over this 10-year period. One of the notable, and reassuring, findings is that nearly 58% of filers who were in the poorest income group in 1996 had moved into a higher income category by 2005. Nearly 25% jumped into the middle or upper-middle income groups, and 5.3% made it all the way to the highest quintile.
And I find this particularly interesting:

Those who start at the bottom but hold full-time jobs nonetheless enjoyed steady income gains. The Treasury study found that those tax filers who were in the poorest income quintile in 1996 saw a near doubling of their incomes (90.5%) over the subsequent decade. Those in the highest quintile, on the other hand, saw only modest income gains (10%). The nearby table tells the story, which is that the poorer an individual or household was in 1996 the greater the percentage income gain after 10 years.
And what about the rich folk?

Only one income group experienced an absolute decline in real income--the richest 1% in 1996. Those households lost 25.8% of their income. Moreover, more than half (57.4%) of the richest 1% in 1996 had dropped to a lower income group by 2005. Some of these people might have been "rich" merely for one year, or perhaps for several, as they hit their peak earning years or had some capital gains windfall. Others may simply have not been able to keep up with new entrepreneurs and wealth creators.

The key point is that the study shows that income mobility in the U.S. works down as well as up--another sign that opportunity and merit continue to drive American success, not accidents of birth. The "rich" are not the same people over time.
How does this study compare to similar studies from the past?

"The basic finding of this analysis," says the Treasury report, "is that relative income mobility is approximately the same in the last 10 years as it was in the previous decade."
While it is nice that socialist countries provide free education, all those taxes, rules, and regulations are barriers to people who want to make something of themselves. They make it a lot harder to start a business. Small business is the engine of the American economy, and it is the key reason it is easier to "move on up to the big time" here than it is anywhere else in the world.

And as Dalaena already noted, our system of grants and student loans is extremely robust in the USA. Anyone who wants to get a college education can get one now - or at least money is not the stumbling block.