To stream or not to stream?

Is streaming legal in Germany?

That’s what I hear / read almost every day now. Why in Germany? Well, because I live there of course, but also because new incomers might have heard about the strong policy Germany adopted against illegal downloads. That thing can frighten you, your family, your cat and even your grandmother. Especially if you come from France, where Hadopi nicely warns you twice before repressing. So I can understand the question.

Legal or not?