For clarity, a safe (or safety) deposit box is a safe in a specially protected area of a bank. The box and its contents are therefore protected from fires and floods, and inaccessible to thieves in your house. Our box is rented by the year, and we pay approximately $100 per year. We can access our box at any time during business hours. The bank doesn't know what's in our box, and the contents are not insured by the bank or the FDIC.
In determining whether you need a safe deposit box, the most important question to consider might be what you keep in it.
According to Bankrate, good things to keep in a safe deposit box are personal and important papers, and valuable items like collectibles and jewelry. U.S. News says that anything important that you don't touch weekly can/should go in a safe deposit box.
Personally, I think weekly is too high a threshold. If you go to the bank often, then monthly might be a workable threshold. However, I do almost all of my banking online, so I go to the bank rarely. Therefore, my threshold is yearly.
And there are plenty of important documents that I don't touch that often or at all - things like our wills, the deed to our house, and so on. There are also a few pieces of expensive jewelry that I would never sell but rarely wear, so those go into the safe deposit box also.
Another thing we keep in the box is a backup of our computers. I use a Western Digital external hard drive to store backups of photos, documents and other files that I would be devastated (or at least annoyed) to lose. My original plan was to have two hard drives and swap out one for the other once a year. However, I go to the bank so infrequently that it's been more like every two years.
Keep in mind that there are items you shouldn't keep in a safe deposit box. These include cash (which is likely expressly prohibited by the rental agreement, unless it's collectible) and weapons (which are also prohibited by most rental agreements). You also shouldn't keep items in the box that you're likely to want on short notice, such as passports and original copies of your will and durable power of attorney. (However, duplicate originals, such as birth and marriage certificates, can be kept in the box.)
In sum, a safe deposit box is a safe place to keep valuables, especially those you don't need very often. If you only have a few items and they're not that valuable, a safe deposit box might not be worth the rental cost. But if you have some valuables that you really want to keep safe, a safe deposit box is definitely worth considering.
As for us ... we'll be keeping ours. I just have to switch out the hard drive backups!