CRIMESTAT is a program that interaces with ArcGIS and other desktop programs. The program itself conducts geostatistical analysis using crime and incident locations and times. The program is used widely across the nation for spatial analysis.
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 Most of this, as noted on the page, has been superseded by the City's own GIS portal, but the community area data should still be good.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.