Open Crime Data Map:
I built an app that ingests the Incident Reports (which are curated by the Police Department), geocodes a location based on the reported address, and assigns an icon to the Incident based upon the category.
The website features a timeline slider so you can view historical incidents or only show newer ones. I like to use this tool at the end of each week to see what has happened in Madison. Once in a while there are some gold mines.