Why people in Germany don't lock their doors? In anime Monster, it's common to see people enter other's houses just by opening a door (without a key). Example: episodes #7, #12.

Why is that?
There is no definitive answer to your question, however here are two points which may answer your question, between the two.

1) The people in question deem the area they live in safe enough to leave their doors unlocked, therefore walking in without a key would be simple.
For example it was a common game with us children where I lived to open a persons door and run away. (I was young, we did stupid stuff). As well as the fact that I and my family leave our doors unlocked when we are home.

2) They forgot to lock it. This isn't as common though also happens. If a person is not a complete safety-enthusiast with a checklist of things to do to ensure their safety, they are bound to forget to lock one time or another.