There is an icon at the moment, but in the console it says that it wants to load another file (which does not exist).
In the source code you can see, that there are several link-tags linking to an old icon. I tried to delete the favicon, uploading another one. I deleted the cache, deactivated caching and optimizing plugins. But nothing worked.
It also causes a mixed content error, when I tried to switch to https. It always wants to load that icon over http, although I changed base URLs AND reuploaded it.
I finally found it. After searching the DB I realized that it was the menu icon (Menu Plus Addon) which was not set. But it still wanted to load it. I placed a new icon and now its working well. Damn, I nearly went crazy yesterday. My fault.