It is not specifically for data from the cognitive sciences but figshare might be worth looking at:
figshare allows researchers to publish all of their research outputs in seconds in an easily citable, sharable and discoverable manner. All file formats can be published, including videos and datasets that are often demoted to the supplemental materials section in current publishing models. By opening up the peer review process, researchers can easily publish null results, avoiding the file drawer effect and helping to make scientific research more efficient. figshare uses creative commons licensing to allow frictionless sharing of research data whilst allowing users to maintain their ownership.
figshare gives users unlimited public space and 1GB of private storage space for free.
(There is more information at their FAQ)
As of now (August 24th, 2012) there is only one data set that is filed under psychology (from an article by Wicherts & Bakker, 2012) but there are several more in the social sciences. Maybe this interdisciplinary repository will grow some more in the future.
