Where is it ok to take pictures? Is it ok in Cathedrals or Castles?
There aren't any general rules. Each cathedral or museum etc will either allow it or post a sign that photography is not allowed. It is usually inside a museum that you encounter the "no photography" signs.
If you can't take pictures, they'll have plenty of postcard books in the gift shop.
We've found that usually the castles that you have to take a tour through don't allow pictures.
There is a third option. Some cathedrals charge a small fee to take pictures.
No photography inside Neuschwanstein or Hohenschwangau. As others have noted, it's an ad-hoc decision by the individual site, and there is no national regulation.
Oh yeah, also, no photography in Aachen Cathedral. All of the churches in Munich are OK (or at least, nobody stopped me).
I've taken photos inside St. Peter's in Baden-Wurttemberg and the Munster in Freiburg. It was allowed.
Sometimes, and I believe it may have been the case with the Munster in Freiburg, you need coins to turn lights on inside the church. So, you may want to make sure you have coins...
Be a good tourist and follow the local rules and signs, as it could be embarassing.
Once. many years ago, I was in a German cathedral (I think, Cologne?) and I either didn't see the no photography sign, or more likely, thought I could get away with it because it seemed there was nobody around. When I started to take a photo, a nun appeared out of nowhere, shook her finger at me, and said reprovingly, "fotografieren ist VERBOTEN, Mein Herr."
I'm older, wiser, and more respectful now.