Domains for countries are called Country TLD's (Top-level-domains), or cTLD's for short.

In general, you need to know your potential customers. For example, if you have a ski-site advertising Austrian skiing, then you probably want the Austrian cTLD -- so local customers there will find your site.

Benefits of country TLD:

1. Customer's browsers may automatically try the TLD of their country, when visiting a site.
2. Higher ranking in search engine's if TLD matches the searcher's country.
3. Higher confidence for site visitors, if they are buying a product online for their own country.
4. If you have multiple TLD's, you can customize the experience for visitors from each country.

Here is a chart of the most popular cTLD's from Verisign.

At this time, the .CN (China) and .DE (Germany) are the most popular, after .COM of course.

Also keep in mind that the .COM TLD is the most important and valuable. A large percentage of users will automatically try YOURSITE.COM, even if they should be going to YOURSITE.COM.DE