Thing is you -do- own copyright to your work when you write it. Even no need to write (c)..., you just do. Simple, easy, fast. But then someone makes a copy and says they are the real author and you are a copycat. So where's the proof? Their word vs your word is a stalemate, so they will certainly try finding some means of producing fake proofs they wrote it. This way, despite the fact the copyright should belong to you, the judge will grant it to some thief, just because you haven't protected your work.
That's why this "sending to self" is encouraged - a sealed envelope can be examined by experts to be authentic. There's date of sending it, which is quite reliable. Basically the post office works as a witness in your case, proving you owned a copy of given work at date stated on the envelope, and unless the opposing side can't produce a proof they had that work earlier, the power of the argument is on your side.
Of course this kind of proof is not a 100% one but may work as a simple, cheap method before you do something serious, and give you time to register your work officially.
So, you don't have to apply for copyright, but if you want to retain rights to your work, you'd better have some good means of proving it -is- your work.