'Corvid' denotes a large family of birds that includes the ravens and crows, as well as magpies, jays, and many other species. Corvids are intelligent, adaptable birds that have been both revered and hated throughout human history. There is a wealth of information on corvid history, biology, behavior, mythology, and more - if you are interested in that, there are corvid-related links at the bottom of the page.
I feel a very close connection to crows and their kin, and have felt that way as long as I can remember. I have worked with wild crows in rehabilitation and educational situations, and captive corvids kept as companions.
One thing I want to note, because it is probably one of the most commonly asked corvid questions that I have encountered, is that it is ILLEGAL to keep any native corvid species in the United States. A special permit to keep them is extremely hard to get, and if you are not a licensed zoo or sanctuary, you are very unlikely to obtain one. Even licensed wildlife rehabbers are usually denied access to them. People do keep corvids illegally, and many people love to share stories of crows or ravens they kept as 'pets' for a period of time. If you do own a native corvid, it can be confiscated and euthanized. The laws are very strict about this, and by taking or keeping a native corvid, you are putting the bird's life at risk.
Also, crows and their kin do not make good 'pets'. They are extremely intelligent and social creatures. They are built to be around their avian kin twenty-four hours a day. Do you have twenty-four hours a day to spend with a bird? The bird will not understand why you leave it to go to work, it does not understand that you have a life outside of your home and time with it. Even if you spent eight hours of the day with a corvid, that is sixteen hours the bird spends alone. Think about that. That time kept caged, alone, is and can be detrimental to the mental health of a very social animal. You wouldn't leave a three year old child in a cage alone while you went to work and visited with friends and family. You shouldn't leave a bird.
That said, there are corvid species it is legal to keep in the U.S. Non-native species, such as pied crows, carrion crows and white-necked ravens are bred and sold as companions, albeit infrequently. If you are even considering this option at all, I suggest learning everything you can about not only corvids, but companion birds as well. Crows and ravens have special caging, health, and dietary requirements that are not only a huge investment in time, but in money as well.
These are a few of my favorite corvid-related books:
Here are some links to great corvid information sources; for fancier, owner, and would be owner as well :