The City of Chicago maintains an informative GIS portal with links to base maps, datasets, and specific interactive maps for various applications, such as airport area sound insulation levels, interactive zoning maps, and West Nile virus infection tracking.
The University of Chicago Library hosts a page with a smattering of Chicago shapefiles for ward district maps of the 90s, police beats, census tracts, and community areas. Most of this, as noted on the page, has been superseded by the City's own GIS portal, but the community area data should still be good. No license is given although there is contact info for a curator.
The Library of the University of Arkansas has a very impressive collection of international and US geodata repository links - mostly geospatial data and attributes. I'll be poking around in here for hours, I think! A wide variety of topics and well-organized to boot.
A project of Columbia University, "SEDACs mission is to develop and operate applications that support the integration of socioeconomic and earth science data and to serve as an information gateway between the earth sciences and social sciences." In addition to a host of interactive mapplications, they host a large number of academic data sets on a wide variety of topics.
"The North American Religion Atlas (NARA) provides access to resources for the study and teaching of North American religious history within a geographical and multimedia framework. Using mapping technology, users can view data on religion at national, state or county levels. Text, image, and multimedia formats are also available and contribute to greater understanding of the story of North American religion."