In the US and many other countries, a copyright is created "the moment it is created and fixed in a tangible form that it is perceptible either directly or with the aid of a machine or device". Stating a copyright in the footer of a website does not mean it's been registered. In fact saying it at all is not required.... it's simply being done to strengthen the assertion of their rights so no one can claim it wasn't obvious or that they read other rights to the work.
Unless a work states that rights are being waived or governed under a less strict license [i.e. Creative Commons, GLP, etc] it is protected with no right to republish or redistribute -- fair use being a claim but not necessarily a granted protection.
Now if you want to make a claim to a name like Google, Amazon, vBulletin you would need a trademark which is a very different set of laws.
Trademark don't require a filing either but are much stronger when you do have a registration [common law mark vs registered mark]. You can search US federal marks at www.uspto.gov although their can be state originated marks too. Filing is around $350 last I checked but while you can do it yourself, having an attorney help makes a lot of sense... just a couple word difference or the wrong class and the effective protection of your mark changes. Not everything can be trademarked either -- uniqueness, novelty and fame all play a role in both registering and winning a dispute.
Remember - forums are great to discuss a theory but should not be used for actual legal advice. I'm not an attorney and don't play one on tv.