Maybe somebody at some time will have the same issue so I'm posting the solution for this.

After long time just living with this issue today I started again to investigate and realized, that the VMware USB Arbitration Service was not running and could not be started. 
My first attempt was to repair the installation of VMWare but even a repair failed. So I had to uninstall it, which caused Windows to repair it's registry, and after installing VMWare fresh the service started and now I have all my USB devices shown to me and I could add them to the virtual machines. 

Lessons learned. If something fails look into your services if all expected services are running.