Yes, crows will strike people. One hit my mother as she was walking in the park, knocking her hat off. Then it settled in a nearby tree and laughed about it.
However, in Canada, the big danger is red-winged blackbirds. They don't like you going near their nests, and they REALLY don't like you wearing red. I went birding wearing a red rainjacket once, and can still feel their little claws in my hair, and hear their ear-splitting shrieks of rage.
I read about someone who used to run along a marsh, and would carry a badminton racket to volley away the blackbirds as they attacked. Gives a new meaning to "birdie," I suppose.