The value of the entire Greek church is in the billions of euros, and nothing is taxed. The government asked them to be taxed a while ago, and the church said that, if they were taxed, they would have to stop charity work because they didn't have enough money. Meanwhile, the high priests wear 30k euro hats and ride around in limousines.
On the other hand, if they did get taxed, a good chunk of it would end up in the pockets of politicians and big companies, as usual. The whole situation isn't very encouraging for citizens who pay taxes...
EDIT: This article [1] mentions that the church put the value of its property at 700m euros. External parties place it at 2-15b euros, while at some point, years ago, 5 monasteries said that they evaluated the value of their properties at around 20b of today's euros (this is just for 5 monasteries). You can imagine how taxing the church would pay off a good chunk of the debt, but, in Greece, you don't get taxed when you have this much money.
[1]: http://dialogoi.enet.gr/post/νάνος-ή-γίγαντας-η-εκκλησιαστικ...