In many cases, you can look up the ZIP code for a street address or city in another country by searching on the website of that country's postal service. For example, if you wanted to find the postal code of a German city, you could search on Deutsche Post's website.
Another easy option is to use an online map application such as Google Maps. Simply search for an address or business name and it gives you the full street address, including the ZIP code. There are also a number of other ZIP code look-up tools, such as GlobeFeed.com's postal code look-up.