The Horatio Alger myth—that hard work and pluck will lift a person from dire circumstances to enviable success—is more than 150 years old, but it has staying power: Forty percent of Americans think it's fairly common for someone to start off poor, work hard and eventually rise to the top of the economic heap.

In reality, however, only 4% of Americans travel the rags-to-riches path, according to new research from the Economic Mobility Project of the Pew Charitable Trusts. And a great many who are born into the poorest segments...