I have tried, with no success, to kill crows with a stick bow. They are a hard bird to hunt, no matter the weapon of choice. The wife has been wanting to mount one so I've tried more times than once to slip up on them in the yard with a bow and make a kill.
Crows are extremely intelligent. My aunt had one when I was a kid and it could talk better than any parrot I've ever heard. There was an episode of Nature a while back on PBS called A Murder Of Crows (fyi a flock of crows is called a murder). On that program, they not only showed that crows recognize different human faces, as already stated, they also have problem solving abilities. They can do 3 step processes in a "puzzle" to receive a reward. Their problem solving abilities and memories seem to be on par or maybe even above those of MOST primates. Amazing birds!