Extra people being born "steal" a lot of the growth, but they create a lot of it too. The GDP per capita figure, according to the Wikipedia article linked to your graphic, grew by only 1.35% per year over the same period.
That's something like 1.2% GDP growth per household, while median household income is going up at 0.5%.
On one hand, there might be less dependents per household, but on the other hand, there's a lot more women working. Despite all the housewives burning their bras, forgoing large families, putting their kids in childcare and getting a job, household income still hasn't risen.
Maybe there's a lot of low-payed single women, dragging the median down. That doesn't convince me that everything is OK though.
Let's look at incomes of income-earning over 15s:
Between 1960 and 2004, the salaries of white males went up 0.068% a year. White women's salaries grew at 2%, probably because they were working much greater hours. Black men did well, and black women did even better. But overall, it was a 0.74% per year increase. http://en.wikipedia.org/wiki/Personal_income_in_the_United_S...
People are better off, but mostly because the women are working longer hours, they don't have kids. Soon, they will also be working more years, as the boomer realize they can't retire. It's a lot better if you're black, but not because of productivity growth trickling down to median workers.
I could track down the numbers, to find how many workers over 15 there are (or maybe how many people there are over 15, or between 15 and 65), but I just don't think productivity growth is <1%, like median income growth. If productivity growth is <1%, then we have another problem altogether.
OK, here we go, real growth by percentile (1960 to 2007):
Arguably (as pg says), this is a good thing, because risk-takers and innovators are being rewarded, driving growth. But it's not as simple as high inequality = high growth, and that doesn't explain why inequality is growing. pg says it's because corporate structures are becoming more efficient, cutting out deadwood managers. Whatever. If this is the case, why isn't GDP growing at a higher rate than the 60s? Has our society simply reached the point where technology no longer drives growth? That's scarier than greedy executives, compliant governments, self-serving boards of directors looting society; but I don't think it's happened yet.
China had huge inequality in the from 1750 to 1950, and stagnent growth, low inequality and moderate growth from 1950 to 1990 (with a few hiccups, notably the Great Leap Forward, and Cultural Revolution, but communism worked a lot better than their previous system of capitalism + corrupt feudalism), then high inequality and high growth from 1990. While inequality might be a requirement for high growth, it's not always a good sign. It can just mean that the rich and powerful are screwing the poor, which makes it harder for a poor innovator to take their idea from rags to riches.
Typical household sizes have shrunk too, so your median household income might well be feeding 2 people rather than 3. http://www.census.gov/population/socdemo/hh-fam/hh4.csv