It depends. In my state, if the original owner doesn't come forward in five years, ownership is given to the person that found it. There are ways to claim ownership of lost money - for example, by knowing the location the money was found and the exact denomination. If you turn in $100 you found on 4th street, and someone else has filed a lost property form saying they lost $100 on 4th street, the police are going to give it to them.
Anyhow, state law here is that any lost property of a value over $50 must be turned in to the police, or there is the potential to be subject to up to $5000 in fines, the loss of the property, and 9 months in jail.
Friend of mine lost his samsung galaxy s5, for about 3 moths later cops called to him and told they found his property (in some raid or something) and they gave the cell back to him. (Because he was purchased a replacement s5 he decided give it to me for free, in turn i handed it to over my gf as a gift, because i'm just a nice guy