I was born in a country that doesn't give out citizenship (A middle eastern nation). My father, too, was born there. In fact, I need a visa to go visit my own birth country (where my parents still live).
I inherited Indian citizenship through my father and his family (I've never lived there), and potentially British citizenship through my mother (she was born in England but British nationality laws are very complicated). I travel on an Indian passport although I can not vote in India as I am a Non-Resident Indian (That might change for the 2014 elections).
My permanent residency, interestingly, is in Canada; and I live and work in the US.
Edit: I just know there is a business in here somewhere.