Despite the "backpacker" stereotype, German tourists overwhelmingly stay in Germany/Europe statistically. For instance, 12,3% of Germans tourists alone spent their summer holidays in Spain and roughly 6% each were on holidays in the German states of Bavaria (mountains, lakes) and Mecklenburg-Vorpommern (Baltic Sea resorts) in 2012.
The most popular destination outside of Europe by percent of all German tourists (as of 2012):
1. Turkey (7,4%)
2. USA (3,7%)
3. Far East (China+Thailand+Japan+Korea) (2%)
4. the Carribbean Islands (1,7%)
5. Egypt (1,2%)
6. Rest of Northern Africa + Middle East (2%)
7. Canada (0,8%)
8. Sub-Saharan Africa (0,7%)
9. Australia + New Zealand (0,6%)
10. Mexico (0,4%)
Turkey is a very popular destination for summer holidays (Antalya, Bodrum) and sightseeing (Istanbul, ancient Greek sites etc.). Also, there are a lot of German Turks who visit their relatives, friends etc. in Turkey.
The USA has always been an important destination for Germans for both visiting and emigrating. Furthermore, there are also many U.S. citizens living in Germany who travel back to the US to visit relatives/friends or spend a couple of time back home. Canada has also become quite popular among students, backpackers etc. I guess the most popular places to go in the region are New York City, Southern California, Vancouver and Southern Florida.
The most popular Far East destinations are Thailand (sex/leisure/cultural tourists, Thai expatriates etc.) and China/Japan (mostly business or cultural tourists). The whole region is not that common as a tourist destination and seen as something quite exotic, though.
Australia and New Zealand (to a lesser extent) are currently THE places to go for many young German backpackers/students/adventurers and possibly more popular destinations than the 0,6% number suggests. There are at least 6 persons from my High school graduating year alone who spent a year working, partying and travelling through Australia after they had finished school. There must be a significant young German presence in many Australian pubs during some time of the year!
The Carribbean Islands are mostly popular for sex tourism, so it's mostly weird old geezers (Punta Cana/Dominican Republic) or their female counterparts (Jamaica, Bahamas) going there.
I guess most German tourists visiting (Sub-Saharan) Africa go to Namibia/South Africa (cultural tourists, adventurers) or Kenya (safari, sex tourism).
Source (German):
Urlaubspläne : Das sind die beliebtesten Reiseziele der Deutschen - Nachrichten Reise - DIE WELT