An Australian accent, of course.
I reckon most Germans can hear that I am not a native German speaker. Funnily enough, when I have spoken about it with various people, the most common guess is that I am from the Netherlands. Having paid attention to the way Dutch speaker sound when speaking German, I can understand that. There really are similarities to my accent. There are not many Australians here, so most Germans have never conciously heard an Australian speaking German. On the other hand, most Germans have conciously heard Dutch speakers speaking German, so they go for the familiar "best guess". I still chuckle though, because I know my Australian accent is pretty obvious to those who are familiar with it.
And that isn't going to change. I speak and write very servicable German, but I am Australian, and I am quite content with that being obvious.
Incidentally, when I speak English with my family, and certain friends, my Australian accent is also very obvious. But given that Australian English is the only variety of Eglish in the world that has remained pure and unadulterated, that's ok.