I have a pretty strong a priori leaning in favour of charter schools. They increase choice for parents and students, and by providing alternatives, they increase the odds that at least some schools will creatively increase learning by students. Those that do not do this will (and often do) eventually fail, something that happens rarely (if ever) in the gubmnt-controlled public school system.
Marilyn sent me this posting from the Wall Street Journal yesterday. It provides a very good, intuitive summary of the evidence that people use both to attack and to defend the achievements of one particular charter school in New York City. Of course since it is written by a person who teaches at a charter school, it may not fully or fairly represent the views of education bureaucrats and teachers' unions, the strongest opponents to charter schools. But it seems to do a pretty decent job.
I'm sure there are more systematic studies of the value-added by charter schools vs public schools. I can imagine cross-sectional and time-series studies that include variables such as family income, family structure, parental education and IQ, and the student's IQ, et cetera, all to try to correct for what otherwise might be thought of as confounding variables that would also help to explain why some students do better than others. Here's a start with the Wikipaedia entry and the lengthy list of references included there.
A national evaluation by Stanford University found that 83% of charter schools perform the same or worse than public schools (see earlier in this article). If the goal is increased competition, parents can examine the data and avoid the failing charters, while favoring the successful charters, and chartering institutions can decline to continue to support charters with mediocre performance.
And that is the key to supporting charter schools. If they don't do the job, they don't succeed.