I think it's important not to overgeneralize based on crime statistics, whatever their source. Keep in mind that criminals today are very mobile... very few probably commit crimes in their own neighborhoods, where people might recognize them! Also, at least in Portland, the neighborhood can change within a few blocks quite easily!
That said, there are still bad pockets scattered about, and you don't want to be caught buying in one of those "war zones" we all hear about. I would recommend visiting the neighborhood you are considering several times during the day and night, and just be very observant. Sit in your car for awhile, and just watch/listen. Walk around, and strike up a conversation with any of the neighbors out walking their dogs or working in the yard. Ask them if they feel safe in the neighborhood, if they know of anyone who was robbed, had their car stolen, if there is a neighborhood watch, etc. Look for signs like grafitti, bars on the windows, run-down houses or overgrown lots, derelict cars, etc. Visit the local elementary school and take note about how many parents drive their kids to school vs walking them, etc. A sign of an "improving" neighborhood, by the way, is to see how many dumpsters there are out front... that means the house is in the process of being remodeled, usually!
In other words, look beyond the numbers. I've got a listing in a great neighborhood, highly regarded, very quiet and safe, but someone told me recently it has "high crime" statistics on Portland Maps. I'm sure that's because it is being lumped in with several nearby neighborhoods, but if you spoke with most of the immediate neighbors for blocks in every direction, you would get a very different picture...