I don't mind crows, but then again they have never attempted to compete w/ my chickens for scraps or food. On occasion several will roost up in the perimeter trees and do their kaw thing.
Crows are super intelligent. As others have mentioned, they love to chase hawks, can recognize the good and bad people in their environment, and have been known to exhibit behavior akin to mourning when one of their comrades dies.
My country boy neighbor said crows will steer clear of your garden and property if you hang a dead crow in plain view of the area in question. While I personally don't advocate killing a crow for no apparent reason, if you happen to stumble across a dead one, give it a try.