The OpenCit project tracks and synthesizes this literature. Overall, they report,
"Recent studies have begun to show that open access increases impact. More studies and more substantial investigations are needed to confirm the effect, although a simple example demonstrates the effect."For more details on this issue see this summary of the ongoing research studies that are exploring the impact of open access scholarship on scientific impact.
Peter Suber has written a thoughtful summary of the state of open access publishing in science concluding:
"While OA [open access] is demonstrably superior for impact, conventional publication is superior for prestige, at least during the current transition period. But there needn’t be a trade-off. We can combine OA and prestige in the same ways in which we combine OA and peer review: a growing number of high-prestige peer-reviewed journals are already OA, and most of the rest already allow their authors to deposit their peer-reviewed manuscript in an OA repository."Nevertheless, the big challenge in opening science is not just opening the "scientific results" to the larger world, but opening up the laboratories and studies themselves. As I have noted in the ongoing debate about "the effect of vaccines on autism" there are powerful opportunities for scientists to contribute to the discussion, but in order to participate effectively we are going to have to move from an expert mode to a participatory mode.