I have owned a few of them - mine were "wall hangers," old damascus barreled double guns, etc. Yes they are legal. Wikipedia says they became required as of GCA 1968, but I think it must have been much earlier than that because I just haven't seen anything less than about 70 or 80 years old without a serial number.
Removing a serial number, or possessing a firearm with a removed serial number is a big time crime. I'm sure you know that but I don't even like posting on this subject without acknowledging that.