I have raised fallen birds from nests before. They were not sick, the roof of our house was insanely steep and there was a covering at the top and birds like to nest there. However, sometimes their chicks did not find it so nice when they tried to fly.
Anyhow, I called our local game warden, told him I had experiance with baby birds (parrots) and that I could handfeed it until it could fly away. He told me that as long as I promised to let it go when it was old enough I could raise it. It turned out to be a mockingbird. We taught him to fly over our bed so when he fell he wouldn not get too hurt. He flew away one day when he got big enough to practice flying outside.
The game warden gave me his name and everything in the event the police for our town ever questioned me (not sure that they would ever inspect houses for wild birds), but thought it was nice.