This is the most extensive and careful study of preschool (pdf) I have seen to date, conducted by Lipsey, Farran, and Hofer of Vanderbilt. The core result is this:

The third question we addressed involved the sustainability of effects on achievement and behavior beyond kindergarten entry. Children in both groups were followed and reassessed in the spring every year with over 90% of the initial sample located tested on each wave. By the end of kindergarten, the control children had caught up to the TN‐VPK [preschool] children and there were no longer significant differences between them on any achievement measures. The same result was obtained at the end of first grade using both composite achievement measures. In second grade, however, the groups began to diverge with the TN‐VPK children scoring lower than the control children on most of the measures. The differences were significant on both achievement composite measures and on the math subtests.

In other words, after some period of time the children who had preschool actually did worse. I found this interesting too:

First grade teachers rated the TN‐VPK children as less well prepared for school, having poorer work skills in the classrooms, and feeling more negative about school. It is notable that these ratings preceded the downward achievement trend we found for VPK children in second and third grade.

So does preschool make kids more grumpy? Immigrant children by the way did well:

…whether or not ESL children experienced TN‐VPK, by the end of third grade, their achievement was greater than either of the native English speaking groups of children.

Arnold Kling offers comment, and for the pointer I thank Peter Metrinko.