There is no global patent office. Patents are managed, protected and enforced on a country by country basis. So ideally, you would file patents for your invention in every country where you think people might want to use your invention. This allows you to enforce your patent rights in these countries. Naturally, this is an expensive proposition, and many inventors decide to file their patents only in the largest markets for their inventions.
In some cases, you may decide to file your patent application in a country which is friendly to your type of invention. For example, business method patents are generally more difficult to file in Japan as compared to the United States, because the Japanese Patent Office (external site) requires that business methods demonstrate some technicity, whereas the US Patent Office (external site) does not impose this requirement stringently.
You should also be aware that if your first filing for an invention is to a foreign patent office, then your country may have laws requiring you to get clearance to make such a filing. For example, inventors resident in Singapore need to obtain clearance (external site) from the Singapore Patent Office (external site) before filing a patent application to a foreign patent office.