Redranger1, you might find yourself in serious legal trouble if you kept a gun you'd "found", and later investigation revealed that it had been used in a crime, or stolen, or something like that. Remember that if you ever use that gun to defend yourself, it will be confiscated from you as evidence and ballistically tested, so that it can be checked against other crime info. The serial number will also be checked against the NICS list of stolen or lost weapons. If any of that comes back positive, you're going to have a heck of a lot of explaining to do... and "I found it!" won't cut it as an explanation for being in possession.
Solution: report and hand in any "found" weapon to the police, and get a receipt for it. That way, you're legally in the clear, and if the gun is unclaimed for a while, you have at least some chance of getting it back, on the basis of "finders keepers".