Good Day ptosis
If the money is from a bank robbery, give it back definitely! You have to figure the serial numbers are recorded somewhere. So the moment you try to deposit or spend the money, you are busted!
Someone might have been mugged on the street. Then, as Pcunix says, the right thing to do, pure and simple, is to turn it over to the police. That person is an innocent, like you and me, who works hard for every dollar she earns.
The money might have come from a drug deal. The guy might have sold illicit narcotics to "earn" that money. In that case you definitely do not want to be holding on to that money. Not only might it be considered "blood" money and all that; but you have to figure he has friends who might come back looking for that money. It seems to me that the thing to do is give the money to the police and ask them to keep an eye on your house for a few days.
By the way, did you see that movie "No Country For Old Men?" The main character (I forget his name), the good ole boy, is out hunting and comes upon a grisly scene in the desert. Two cars wrecked, six people and a dog are dead. Then this guy (played by an actor named Brolin), brain trust that he is, decided it would be a good idea to take the suitcase full of money to keep for himself and his wife. He thinks he can just take the money and he and his wife can live happily ever after.
Well, we see where that got him.