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 Most of this, as noted on the page, has been superseded by the City's own GIS portal, but the community area data should still be good.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.
Movesmart.org is a new website and nonprofit organization dedicated to helping housing seekers find neighborhoods that meet their needs while at the same time promoting diverse, healthy, and vibrant communities. The organization's core offering is an interactive mapping application called Neighborhood Finder (launching late summer 2009), which provides a geographic interface to many different types of data about neighborhoods. Other resources include a series of informative guides about relevant housing and neighborhood topics and a blog about fair housing and other similar issues.
You can learn more about Movesmart.org, as well as watch a short video about the organization and the website, by visiting http://movesmart.org/about (new window).