I just wrote a longish post about how income mobility in the United States is actually pretty anemic, but our blog software ate it and I don't feel like trying to recreate it. So here's the nickel summary: despite what Florida senate candidate Marco Rubio says, America isn't the only place where you can start a business in a spare bedroom. In fact, whenever you hear a politician say "only in America," it's an almost certain dead giveaway that they're blowing smoke. On the specific question of rags to riches stories, the fact is that America has less income mobility than most other rich countries, and that mobility has been declining for the past several decades.
There's a longer version of this, but you'll just have to pretend that I wrote it and you read it. In the meantime, take my word for it. Or, if you don't trust me, take David Frum's word for it.