There are some items that are very important and do need to be kept safe but should not be kept in a bank safety deposit box. They are as follows:
The only copy of your will. People may know what your final wishes are, or that you have a will, but making it exceptionally difficult to fulfill your final desires is not a good idea. Family members may need to seek a court order to have your box opened in order to access your will and this can cause delays in handling your estate. The same advice applies to living wills. These are missives to other people about your wishes, so do make sure people can access them.
Random valuables. Make sure to inventory everything that is in your safety deposit box and have accompanying appraisals -- don't just drop in valuables.
Cash. Safe deposit boxes are not federally insured and you cannot earn interest on cash in your box. For emergency situations, keep cash at home.
Inside the Box
The following items are ideally stored in a safe deposit box:
Inventory of possessions. It's good to inventory household items in preparation or an emergency. When something happens you may be too frazzled to recall all you need to for insurance purposes.
Passport. If you are an infrequent international traveler, keep your passport in a safe deposit box. These are increasingly difficult to replace, so if you don't use it often, don't keep your passport lying around.
Deeds and titles. You will only need the deed to your home and the title to your car when you attempt to sell these items. As such, keep them safely locked up in the interim.
Stocks, bonds, certificates. If you still have any paper stock or bond certificates -- most are issued electronically now -- copy them and put the originals in your safe deposit box.
Rarely worn jewels. Did your mom give you a diamond tiara that you just can't find a time to wear? Get it appraised and lock it away.
Use your judgment and modify this list according to the needs of your life. Keep in mind that safe deposit boxes are deliberately difficult to access, which can be great. But not everything needs to be quite that safe.