You own copyright to the image the moment you press the shutter according to federal law. An extra precaution would be to register images with the copyright office, which is time consuming (and not free). You'd worry about that if you have a lot of images around the web and press and afraid someone might use them without retribution, but even in that case it doesn't mean it'd be worth your time and money to fight them.
I'd recommend searching this forum as the topic has been discussed extensively in the past.
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