The most influential are the Perry Preschool Project and the Carolina Abecedarian Project. Those are two randomized trials, conducted in 1960s Michigan and 1970s North Carolina, respectively. Participants have been followed ever since so as to ascertain long-term outcomes in terms of things like incarceration rates, teen pregnancy, average education level, average income, and more. Because the studies were randomized, we can know beyond a reasonable doubt that any significant differences are due to the influence of the preschool programs.
Both found huge economic and social gains to high-quality preschool. The upfront costs of each were relatively high, with Perry costing about $18,000 a year initially, but the return on investment was, as Obama said, enormous. The best work on Perry, in particular, has been done by James Heckman, an economist at the University of Chicago who won the 2002 Nobel prize for his work on improving econometric methods. He put those skills to use evaluating the benefits of preschool programs.
Heckman and his coauthors started from the observation that those who received preschool in the Perry experiment ended up earning more money — and thus paying more taxes — as well as using fewer criminal justice system resources (because they committed fewer crimes) and receiving less in the way of welfare, food stamps and other transfer payments.