Safe deposit boxes are a good place to keep your important papers and items you may not be comfortable keeping at home. The bank can not claim any of these items, in any circumstance. If you forget to pay your rent, the bank ususally flags your box and will not allow you to access it until the rent is paid. If you do not pay your rent in five years (depending on the state) it is considered abandoned property and is escheated to the State in which the bank branch is located.
There are a couple things you may want to keep in a safe deposit box: Life Insurance, Home insurance documents, antiques or evening jewelry, selected collectables that are more valauble kept safe than on display.
There are a couple things you may not want to keep in a safe deposit box: Wills - once a bank knows an owner of a box has died, some states require the box to be frozen until probate is started - you can't always start probate without a will, (you can see the circle).
Contents of a Safe Deposit box are NOT FDIC insured nor are they covered by the bank's insurance policy. You should continue to insure any item you place in the box. The bank has no knowledge of what you place in the box. In the unlikely event of a catastrophy, (fire, flood, earthquake, terrorist act) the vault may not survive and the contents may be lost.