As far as the U.S. goes, you all are right that it's illegal to keep crows as pets. Well, it's legal if you have a permit to do it, but you won't be able to get one. This is all federal law, as determined by an amendment to the Migratory Bird Treaty Act in the early 1970's. So, it's not a matter of being in the right state, either.
American law on the keeping of animals is strange. In many states you can own mountain lions, African lions, tigers, baboons, chimpanzees, etc. Lots of people own such animals; it's estimated, for example, that there are many more tigers in private American hands than exist in zoos and in the wild. Every couple of years, one reads a story about a jogger somewhere in southern Ohio who is injured by someone's loose tiger or lion. (How angry would you be to be injured by someone's African cat, for chrissakes?) Often you need no permits or license for these animals. But you can't have a pet crow.
Like many federal regulations, though, the government doesn't really have any effective means to enforce the prohibition on pet crows. So, there are plenty of them out there.
Many people who have rescued and hand-fed these birds keep them as pets. Often, these people let the crows fly around freely. In fact, all the pet crows I've heard about or seen live this way. Many such birds will stick with the human and his/her family of their own volition; there are stories of the birds flying back and forth calling while the kids are outside throwing a football around, that sort of thing.
I suppose you'd have to watch out if you lived in a rural area, as I do. Hunting crows is permitted in many states (one exception to the federal protections is killing birds to protect agricultural product). Farmers shoot a lot of crows. If your bird strays too far he might get capped.
Even hand-fed crows have been successfully released into the wild. That's something to consider doing.
Captivity for such a bird is a mixed bag. On the one hand, they're protected from violence, deprivation, and exposure. They could live much longer than they would in the wild. On the other hand, there are all of the frustrations that a captive bird is going to experience compared to his wild counterparts. Exactly how an aviary crow would behave, I just don't know. Problems that some of the larger parrots have in captivity are some guide, I guess. So, without knowing much about it, I suppose I would worry that a captive crow might pull feathers, bite, get cranky with its humans, become listless, that sort of thing. Still, I wouldn't have too much confidence that parrot behavior is predictive of crow behavior.
B 
