Here is what I have gathered so far about the legality of wand use:
- Underage magic is expressly forbidden, except when receiving magical instruction. This probably includes home-schooling (like Ariana Dumbledore).
- Some expulsions from a magical academy (like Hagrid's expulsion) can result in the breaking of your wand and apparently a ban on future use of one.
- Drop-outs like Fred and George, and other expulsions like Newt don't necessarily result in a ban on magic.
- Criminals who are later released from Azkaban may have their wands restored to them, or at least don't get their wands destroyed upon incarceration. Bellatrix's wand along with many other Death Eaters' wands were not destroyed as evidenced by their use of them after escape/release, though that may just be a privilege of the rich, connected, and the later because the government was corrupt.
So how does this work exactly? Hagrid didn't necessarily have his wand broken because he committed a criminal act, but maybe it was a combination of that and his age. Or that and the fact that he had not, and would not, receive sufficient magical instruction. Is there some definitive line we can draw that indicates when someone will be allowed to regularly use magic and where someone won't? Additionally, can we assume that in all cases of a permanent ban on magic, the charged will have their wands broken, assuming the authorities can obtain the wand and due justice is served?