It is important to understand that a right over a trademark is a restriction on commerce. Once a trademark is granted to a market the others may not use an identical or substantially similar trademark to mark the same class of products.
Now since trademark owners must use its trademark to keep their rights and since trademark law is regulated mostly State by State it is not possible to protect a trademark unless you really participate in all demographic markets of the world, like Coca-Cola, although there are places of the works where Coca-Cola is not sold.
There are some internal systems which allows you to protect a trademark in several countries with one registration. Nevertheless, if you don't really use that trademark in each of those countries you may end up loosing it because trademarks must be used.
Finally, keep in mind that if you want to protect your trademark globally you will need to have a good trademark protection and prosecution strategy.
Source: Quora
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