LAPD Crime Maps
This Google Map from the Los Angeles Police Department’s (LAPD) E-policing program shows up-to-date crime statistics for neighborhoods throughout LA. The LAPD say that "being informed about crime in your community is the first step in preventing future occurrences" and they hope that this map will go some way to informing you about crime in Los Angeles.
It is possible to search the crimes by date range and type of crime. It is also possible to adjust the range within which you wish to search.
Previous LA Crime Maps
The LA Times Homicide Map - This mashup from the LA Times chronicles every homicide in Los Angeles County. This map has an incredible array of filters with which to query LA murders.
CrimeReports - Although CrimeReports is not exclusively concerned with crime in LA it is possible to use its maps to search crime committed in the city.
SpotCrime - Similarly SpotCrime produces Google Maps for a large number of locations in the US. Los Angeles is just one of the cities covered by SpotCrime.