In today's New York Times there's an article about multigenerational households. That's where grandparent, child, and grandchild all live under the same roof.
This generally remains a living arrangement for the poor. The rich will buy their children their own place because the rich understand that there is a big loss of status when young adults live with their parents and they don't want their children to sink in status.
There are several converging trends causing the increase in multigenerational households.
(1) Immigration. Immigrants from Latin American and Asian countries don't realize that multigenerational households aren't the American way.
(2) Increasing out-of-wedlock births. It's the norm for black children to be born without their mother being married, but this trend has also become common for white women. "Births to unwed white mothers were 22.5 percent in 2001, compared to 2.3 percent in 1960." (Source: WaPo article). Single mothers need more help from parents and have less resources available to live on their own.
(3) The declining economic status of young people. Even when women are married, a young husband can't provide as well as he used to. The median real income of young men has been declining. Yet if you look at this U.S. census table, you will see that the median price of a "home" has risen by a huge amount. In year 2000 dollars, in 1960 the median home cost $58,600, and that rose to $119,600 in 2000, an increase of 104%. (Unadjusted for inflation the home in 1960 was only $11,900--damn that's cheap!) The 104% rise in the median home price doesn't even take into account the big rise in housing prices since 2000.
Rising home prices represent a big transfer of wealth from the young to the old, because the average homeowner is older than the average non-homeowner, so the older generation grows richer because of its home ownership while the younger generation has no capital appreciation but faces declining incomes.