In 2003, Congress created the first federally funded voucher program in the District of Columbia. This program offered students $7500 scholarships to attend private schools in the area (a number which is significantly below the public schools' per pupil funding rate). When the funds were appropriated, Congress also set aside funds for studying the program. The most recent results were just released; you can read the executive summary here.
The verdict? Vouchers do work -- sort of. Students using the scholarships earned reading test scores that were significantly higher than comparable students remaining in the public schools. This worked out to the equivalent of being about three months ahead in school. Parents also reported higher levels of satisfaction with the schools. However, math scores were not higher with any statistical significance. Scores were also flat for students who entered the voucher program after attending schools designated as being "in need of improvement." Since vouchers are usually billed as a way to help children escape failing schools, this lack of progress is certainly disappointing for some voucher advocates.
However, I view this all more through the lens of being interested in high achieving students. The DC scholarship research study was carefully designed to counter the selection bias critics usually complain about with voucher programs. Kids and families who are most interested in receiving a scholarship to attend a private school are naturally more interested in school -- and hence will likely do better on tests regardless of where they attend school. So this study compared students who didn't win the lottery for vouchers with students who did, not with "regular" students in the public schools. But even if these students would do reasonably well regardless of where they attended school, so what? I'm all for giving kids who want to broaden their opportunities any chance possible to do so. It's too bad all the students who applied couldn't be given vouchers - I like the idea of families being able to look around at the widest variety of schools, and pick the ones the best fit their needs.