“They” say you don't have to register copyright for an item to own copyrights for that item, and technically you do not. But, you cannot sue someone for copyright infringement unless you have registered for copyright for that item. So basically you are technically protected even if you don't register, but you aren't legally protected unless you do register. Once you are registered then you can sue someone for copyright infringement, but you are only entitled any profits they made from items that they gained from your copyrighted material.
If you register for copyright within 3 months from it being published you get additional benefits. You can be reimbursed for attorney's fees and receive statutory damages from the party you sue. If you don't register within that 3-month window you are not able to receive either. You are only entitled to the profits mentioned above.
It is in your best interest to register any original works, including software that you develop, as soon as you publish it.
After speaking to my lawyer I have found that it will cost me in the 10's of thousands of dollars range to bring a copyright infringement case against another party if we actually go to trial. If I win, I would only be entitled to profits that they made from my material because I did not register for copyright within 3 months of publication. The party in question may not have made more than a couple thousand dollars from my work. So I may end up spending 10x more than I am due to win. It's really not about the money, but I don't want to spend a boatload of it just to get someone to stop claiming my work as their own.