It is not technically necessary in the United States to apply for a copyright, but if you are serious about wanting one, it is an extremely good idea. Without the formal application, it is much harder to prove you wrote the song, or software, or whatever. Also, without proof of application, you can't recover damages for infringement.

I strongly suggest you not go out and read the statutes, as statutes can be extremely misleading if you do not have the background and case law. Talk to a lawyer, or if you are really into doing it yourself, find a copy of Nimmer on Copyright. In the Western U.S., in any case, such things are open to the public in your County law library.

I also strongly suggest you take with a large grain of salt things you will find in the many, many copyright threads on this website. They tend to be written by people with axes to grind, and could be v. misleading.