Obtaining a patent in any given jurisdiction (US / EU / Japan etc.) will only secure you rights within the geographical limits of that jurisdiction. It has no immediate effect whatsoever anywhere else.
However, a patent application filed in one place can be claimed as priority for an application elsewhere. For instance, you could file in the US and then claim that US application - with its filing date - as priority for a subsequent application in the EU. However, this is only possible within 12 months of the original filing date. (You can get a longer waiting period between original filing and priority claim by going the PCT route, which however does not directly secure you any rights anywhere.)
Another, more subtle effect of a national filing is that the published application will quickly enter patent literature databases worldwide (18 months after filing). It can then be easily found by most patent offices in prior art searches, and can thus prevent others from obtaining a patent on the same invention - everywhere, not only in the place of original filing.