The NYPD release monthly crime totals at the precinct level, recent statistics are available for felonies, misdemeanors and violations as are historical tables from 2000.
Incident level statistics, including misdemeanors and violations, are now available. Records and locations of complaint data from 2006 are on NYC OpenData, the most recent year is here.
City-wide data for 311 calls are also available on NYC OpenData, as are emergency 911 calls, arrests, motor vehicle collisions, and shootings.
For GIS users, Columbia libraries have prepared spatial files available through GeoData@Columbia for precinct level crime data, complaint data, 311 calls, 911 calls, collisions, arrests and stop question and frisk data for select years.