Washington, DC can boast of greatly reduced crime of every type. The city is quite safe, thanks partially to the fact that many agencies are based there- if a local police officer isn't around, chances are that a uniformed or undercover FBI, NSA, CIA, Secret Service, Park Police, Capitol Police, Metro Police, or other peacekeeper isn't far away.

That being said, as with any large city, normal precautions should be taken, i.e. secure your purse or wallet, stay in well-lit areas. In addition, some neighborhoods are not safe for travel after dark.  Generally, any place a tourist would be interested in seeing, is in a safe neighborhood.  The unsafe neighborhoods have nothing to offer tourists.