Ditto @DaleHartleyEmery. Copyright is a form of property right. You don't have to apply for the right to live in your own house and lock the door against strangers, you just have it. Same with copyright.
Yes, it costs money to register a copyright, but not that much. In the U.S., I think my last book cost me $35 to register, plus you have to send the copyright office two copies of the book. You just fill out a form, which today you can do on-line, and send them the fee.
There are two big advantages to registering your copyright.
(a) It is strong evidence that you did indeed write the book on the date you claim. If you don't register, someone who steals your book could claim that he wrote it, and how would you prove otherwise? I often hear people talk about various schemes to prove they wrote the book, like mailing a copy to themselves and never opening the envelope, leaving a copy with a lawyer, etc. None of these alternatives have the same weight in court as registering, and many are more trouble and/or expense than registering.
(b) It gives you extra legal protection. For example, in the U.S., if you don't register your copyright, you can sue for actual damages, but not for punitive damages. i.e. if someone steals your book and costs you $1000 in lost sales, without registering, you could get your $1000 back. With registering, you could get $1000 plus possibly another $2000 in punitive damages plus if you're lucky you could make them pay your lawyer's bill. (I am not a lawyer, this is just an illustrative example.)