Ask HN: Do I need to register a copyright?

I'm trying to understand the laws around copyright, but none of the resources I've found have given me a very good answer.

If I create some work (a website, let's say), I automatically have a copyright on it. If I register that copyright, then that apparently helps a lot in the case of an infringement case.

But what if I don't register the copyright. What happens if someone copies my work? Can I still take them to court?