My operating system (Elementary OS Luna) comes with a set of wallpapers - one of which is some kind of castle or cathedral built in mountains. Where is it?
The background is called 'Temple' by Jason Absolom. It was one of the announced wallpapers chosen in a competition for the selection of them.
I believe it is a composite image and not a real place, which is why I'm putting this as an answer, but if I'm proven wrong I'm happy to remove it.
It's quite certainly a composite. Building on @MarkMayo's answer I figured tin eye might help and it did. Sadly the original image is a stock image and seems hard to find the origin. From some of the places the picture has been used here it seems likely it is in the Tiroli alps.