By law, if you created the work, you own the copyright - automatically. As the copyright owner you and only you have the right to grant or deny permission for others to copy your work, whether or not you file any forms with the Copyright Office. In the vast majority of situations, the most practical approach is to simply archive a set of dated photographs of your work.
Registering your copyright does cost money (a minimum of $35 per application) paid to the Copyright Office. Registering provides an official date and legal foundation that you own the copyright.
But here is the real problem! Whether you register your copyright or not, if someone starts copying, i.e. infringing, on your copyright, the burden of stopping them is entirely your responsibility. You will need tons of money or a lawyer in the family - or an amazingly good case so that a pro bono lawyer will take on your case for free. All of these are possible but not likely for most of us. You have to be willing to invest a lot more than the registration fee to seriously defend your work. At a minimum, you should send a "cease and desist letter" either on your stationery or the stationary of your lawyer to see if this will scare off the offending party. You can send a "cease and desist letter" as the copyright owner whether you registered or not.
So, should I register my copyright? Is it worth it? If you believe that your work will be duplicated commercially, then I would recommend registering your copyright. Otherwise, I have a few suggestions and alternative perspectives in Part 2.
This post was updated on December 22, 2021, to provide current links.