Just to be clear, as Jo says, copyright is inherent -- as soon as you write something, it is copyrighted; you don't have to do a thing.
Disputes over out and out copyright theft would usually surround who wrote what first. Accordingly it's sensible to have a clear trail of your work -- if you can prove your first draft was written in 2010 you would (well, should...) still win an action if someone stole that draft and published it in 2011 even if you didn't publish your final version until 2012.
In English law there's no need to register anything anywhere. However, from the little I've gleaned of US law, I think the formal registration of copyright is required if you want to seek damages (ie financial compensation) from the copyright thief. Since that means taking legal action to try to get the money, I'm not sure that in reality it's a step many people would take.
And never forget there's no copyright in ideas, only in the execution. There's nothing to stop someone taking the basic plot of your novel, even some of the very original SF ideas, and building his novel upon them. Copyright is there to prevent someone lifting whole passages of prose from your work and making only minimal changes. Though even then, it goes on, see
this thread.