Personally, I think that everyone needs a safe deposit box. If your home ever gets broken into, you won't have to worry about items like your social security card, birth certificate, or passport getting stolen. You can also keep personal items, like photo negatives, in your safe deposit box so that you won't lose all of your mementos in the event of a disaster like a fire or flood. A safe deposit box is also a great place to keep a copy of your home inventory so that you can prove the value of your possessions if you ever need to file a homeowners or renter's insurance claim.
There are some definite drawbacks to having a safe deposit box, though. If you need something that's in the box, you can only access it during bank hours. Then you have to leave home, wait in line, and sign in to be able to access it.
If you're the only person authorized to access the box but you need something from it and have no way to get to the box, you'll have to deal with some paperwork in order to add someone else to the box. Once you've done that, you'll have to worry about whether you can trust that person both with the contents of the box and the ability to not lose the key (there's always a charge for losing a key, usually $25 or so). Also, safe deposit boxes aren't free, of course. Depending on where you live, which bank you use, and the size of box you choose, the fee can vary quite a bit. Where I live and bank, I pay $50 a year for the smallest box, which is something like 16" x 5" x 3".
Of course, even putting your valuables in a safe deposit box at the bank won't make them completely safe--just ask the folks in New Orleans.