Logos do not have copyrights as they are not supposed to be copied - they are trademarks. A trademark accrues automatically once you start using a 'mark' (logo, slogan) in 'trade' - you don't really have to do anything except put the TM symbol to claim a trademark. But if you want to be really sure, you can 'register' your trademark in your country, and put a R symbol. This will help you in case your trademark is challenged, especially in court.

Historically trademark protection laws have been used to prevent Brand B from marking their products deceptively as Brand A, and benefiting from Brand A's painstakingly created goodwill and expensive marketing.

As far as copying trademarks go - if it's registered, and you're in the same business, don't even bother. If it's only a TM (not R) and you're in a different business, it could possibly work if the other brand is not careful about catching you at it early.

You can possibly be sneaky and start using it. If your product becomes more successful and generally more recognized than the other product, the trademark can become yours (albeit via an expensive process of suing). But honestly, it could go both ways. Don't do it unless you're Apple Computer, Inc.

On the whole I'd say just don't bother with it, it's not that difficult or expensive to find a freelancer and have them make your own logo.

So you are saying that in order to put the TM on your logo, you don't need to pay or make papers with an organisation?