Examine the resources here for Case Studies and other Research based articles applying GIS to any of a number of scenarios.
This map shows how GIS was used to capture a sex offender based on their activity in Toronto
Image obtained from: http://www.miller-mccune.com/legal-affairs/gis-cops-favor-new-kind-of-plotting-4464/
Covering a broad range of subjects and topics for numerous disciplines, these resources are a good place to start your research.