Why, you might ask, should you not offend a crow? (Other than the fact that they’re smart [and smart-ass] birds who deserve a little respect, that is.) Well, the crow may remember your face and hassle you every time you show it in his vicinity. Furthermore, he may alert other crows to the fact that you’re a dangerous element, and they may hassle you too.
This New York Times article describes the work of John Marzluff of the University of Washington, who has established that crows and other corvids recognize individual human faces. His experimental procedure involved masks that were used to isolate facial recognition from other unique aspects of humans appearance such as dress or gait. Some of the masks were initially worn only by people who were catching and banding crows (which made them bad guys, as far as the crows were concerned), and others only by people who were going about their business without bothering the birds. Later, when people wearing either a bad-guy mask or a neutral mask walked around on campus not pestering the birds, the crows heckled those in the bad-guy masks more than they did those in the neutral masks.
In one case, a professor wearing the bad-guy mask got a reaction from more crows than had originally seen the capture and banding that had earned the face its bad reputation, indicating that the birds were learning from each other which hominids were less than desirable.
To read the original work, check out Lasting recognition of threatening people by wild American crows, a paper by Marzluff and his colleagues in Animal Behavior.