I was looking for the free VMware Player, which was available for quite some time.
Turned out, the free Player still exists - but is now called "VMware Workstation Player (formerly known as Player Pro)".
If you got to this website: http://www.vmware.com/products/player/ - you will find a lot of text about some paid version - but if you look up closely to the last paragraph "VMware Workstation 12 Player Free for Personal Use" - you will find the text "environment you may use Workstation 12 Player at no cost.
Download Workstation 12 Player for personal use." - and the "Download" writen in faint blue color - yep - that is a somehow hidden link. Click it! ( Hint: https://my.vmware.com/en/web/vmware/free#desktop_end_user_computing/vmware_workstation_player/12_0 ) - And there you will be able to download the latest version for free.
Bonus: The compatible VIX 1.15.2 API can be found here: https://my.vmware.com/web/vmware/free#desktop_end_user_computing/vmware_workstation_player/12_0|PLAYER-1210|drivers_tools
Update: For VMware Player 14, the link changed to: https://my.vmware.com/en/web/vmware/free#desktop_end_user_computing/vmware_workstation_player/14_0