People tend to forget that Japan isn't called Japan in Japanese (it's called Nihon) or that Germany is actually the Budesrepublik Deutschland to the Germans, but these endonyms are an important part of a country's identity.
An endonym is the name for a place, site or location in the language of the people who live there. These names may be officially designated by the local government or they may simply be widely used.
And yet the average map doesn't include these endonyms, so people are left wondering what a suomen tasavalta or rzeczpospolita polska is when they see it written somewhere.
At Endonym Map you can see what all the countries of the world call themselves in their official or national language, on a large, nice looking map which the site is constantly striving to improve:
The vast majority of names come from the United Nations Group of Experts on Geographic Names and the U.N.'s database of country names. Other sources include the CIA World Fact Book, Wikipedia and various government websites.
One big change I am exploring is the inclusion of minority language endonyms in some fashion. I would love to put all three official languages for Belgium on the map, or both Ireland and Éire for that matter. But with the limited space on a fixed map, there's just not room to do it fairly for all countries. And it bugs me to no end that places like South Africa and India have a dozen or so recognized languages, but there's only room on the map for one. But I am working on it and hopefully will come to a solution soon.
In the meantime, please enjoy the map!