Finding unclaimed money from banks and investments
It used to be that if a bank went out of business, people who had money deposited there might lose some or all of their money. In the movie It's a Wonderful Life, for example, a rumor causes everyone in the town to try to withdraw their money from the bank all at once. Banks don't keep deposits in cash; instead, they invest those funds by loaning them to people to mortgage houses or to start businesses. So if there's a run on the bank and everyone wants their deposits back all at once, the bank may go out of business.
Now the Federal Deposit Insurance Corporation (FDIC) protects depositors in most cases in the event of a bank failure. If a bank you had money deposited in went out of business, the FDIC may be holding unclaimed money for you. You can search at https://closedbanks.fdic.gov/funds/
Likewise, the National Credit Union Association protects depositors in credit unions. Search for unclaimed credit union funds here https://www.ncua.gov/support-services/unclaimed-deposits
Finding Unclaimed Money from Investments
If a savings bond you had was lost, stolen or destroyed, you can file a claim here http://www.treasurydirect.gov/indiv/research/indepth/ebonds/res_e_bonds_eereplace.htm
If the Securities and Exchange Commission recovered money for investors from an enforcement action, they may be holding and distributing those funds. If you believe you may be owed funds from such an event, you can find out more and search here http://www.sec.gov/divisions/enforce/claims.htm