Is it true that the only way to take legal action against software copyright infringers in the U.S. is to first register with the U.S. Copyright Office? And is it true that that's the only way to recover statutory damages?
In the United States, copyright is attached as soon as the work is created. Registration is not necessary unless you wish to seek statutory damages against an infringer 1. You can seek litigation and actual damages without registration. However, registration does provide a legal record that can assist with matters of litigation of all kinds.
Are there other benefits of registering software with the U.S. Copyright Office? What are the costs, besides the fee and the hassle of re-registering new versions of the software?
I would recommend consulting a lawyer who specializes in intellectual property or software law. There are a lot of reasons why you might want to consider registrating versus not registering, and a lawyer with this expertise would be best suited to help you determine the best course of action to help you legally protect your work.
1: There appears to be some confusion on this point. Most sources that I've found say that the Berne Convention allows you to seek actual damages from an infringer without copyright registration. However, [Robert Harvey links to a document from the US Copyright Office] that says registration allows you to file infringement suits, possibly indicating that registration is required to file any kind of legal action in the United States (a signer of the Berne Convention). Best course of action: Consult a lawyer, specifically an intellectual property or software law specialist.