The answer to that is complicated, and depends in large part on the country.
HBO does have a number of branches, partners, subsidiaries, and affiliates abroad, who take all of their programming. All of those will be showing the series.
In Canada, the show will be seen on HBO Canada, same days and times as in the US.
In Brazil, Argentina, Mexico, Colombia, Venezuela, Peru, and Chile, the series will be shown on HBO Latin America, though days and times may vary.
In France, GAME OF THRONES will be shown on Orange.
In Israel, on DBS.
HBO Central Europe will offer the series in Poland, Hungary, Bulgaria, and the Czech Republic.
HBO Asia will offer the series to the countries in their territories, though which ones will pick it up and when they will show it remains to be confirmed. There may be content questions in some Asian markets.
In some of these countries, HBO is a premium channel, as in the United States. You have to sign up and subscribe to it (and pay for it), it is not one of the channels you get for free just by turning on your television.
As for the countries not listed here... next week in Cannes there will be a huge television trade show attended by broadcasters and program directors from stations all around the globe. HBO will be there, screening its new shows and selling them. GAME OF THRONES will be one of the series whose rights will be on offer. In a few more weeks we should know which countries bought the series... and which did not. Let's hope your favorite station is one of those to pick it up.