Crows are opportunists and will eat anything that won't eat them first and will fit down their throat. And that includes day old chicks. So keep that in mind.
I still remember a few years ago, hearing an odd screeching sound as a bird flew overhead. After staring at it for a few seconds, I realized it was a large crow, and it had a small animal in its beak. It was probably a young squirrel, and it clearly wasn't dead yet. Circle of life and all that, but it wasn't a pleasant thing to witness.
Over the years, I have lost a few even full-sized hens to hawks; they will even attack birds under cover if they see them run to it. I have lost a few bantam birds to owls, but that was largely because they were sleeping on top of their coop rather than in it.
I have also lost countless eggs to crows. Crows are very clever; they watched all the places the hens were laying and scolded me if I got to the eggs before they did. It got so bad, I began to wonder why I was keeping chickens at all, since on some days, the crows got every egg, and I got none. It was more the foxes and raccoons that made me decide to stop free-ranging, though.
We still have crows around here; I often see several of them wandering around in the pasture, though exactly what they are looking for, I don't know. A couple of weeks ago, my daughter and I saw an incredible number of crows mobbing something (I'd estimate over 100). We have owls, too - I hear them calling in the woods every night (that may have been what they were mobbing, but the owls are still here, so the crows didn't drive them off). The hawks come and go; it's mostly during the fall that we see young hawks out there. It's kind of nice to be able to watch them just doing what they do, and not have to worry that it's my hens they are watching. Kind of nice not having to beat the nest robbers to the eggs, too.

We all have to come to some sort of compromise with the wildlife; I've found one that works for me, I hope you find yours, too.