In the United States, anyway, as soon as you create some original work, provided it's not a work for hire, you own the copyright. It's straight from the theory of property by John Locke--the British philosopher, not the bald guy from Lost.
So what you really want to do is not to copyright your work (congrats, you already have it!), but to register your copyright. The place to do that is the US Copyright office.
You don't have to register your copyright, but the $35 fee is a small price to pay to settle future disputes.
For example, say you write a novel and let someone read it. That person might turn out to be a scoundrel who goes to a publisher and claims he wrote the novel. It's published, the guy gets rich and famous, and you get nothing. So you go to court. Among the things you have to prove is that you are the copyright holder. This goes much easier if you registered your copyright with the Copyright Office than if you didn't, because
In any judicial proceedings the certificate of a registration made before or within five years after first publication of the work shall constitute prima facie evidence of the validity of the copyright and of the facts stated in the certificate. 17 USC 410 (c)But beware, dear creator, of some potential technical difficulties waiting for you at the Copyright Office website:
