The Trinity College Library provides access to several repositories that collect aggregated data relevant to multiple subject areas. These are excellent resources for beginning your exploration of data, especially if you're not quite sure what exactly you're looking for.
ICPSR (Inter-university Consortium for Political and Social Research) maintains a data archive of more than 250,000 files of research in the social and behavioral sciences. It hosts 21 specialized collections of data in education, aging, criminal justice, substance abuse, terrorism, and other fields. Users must register to download data.