There is no sole public resource that has compiled crime reports by zip code. The information is available, however, and needs to be properly researched and evaluated.
This particular tracking resource has not been cohesively complied to date. This may be due to the fact that police jurisdiction that report the crimes do not always follow zip code divisions. One zip code may have many police departments and one jurisdiction may be part of many zip codes. However, the FBI compiles data from local police and allows you to view this information online, breaking it down by state or even FBI branches.
Though crime information is not readily available by zip code, all that is required to gather it is to combine information from two or three public sources. To find this, the researcher must first determine what municipalities fall within a particular zip code. From there, one can find the crime data from either the city's police reports or from the FBI's public database.
There are also services that display crime reports by location. This information can be taken and overlain with a map of zip codes to show the distribution of crime. The limitation of this tactic is that these sources tend to only display recent crimes.