Apple - Is it possible to run VMware Fusion in the background to hide the windows and icons it produces?

It appears you can start Fusion headless by executing the following:

/Applications/VMware\ Fusion.app/Contents/Library/vmrun -T fusion start ~/Documents/Virtual\ Machines.localized/[IMAGENAME].vmwarevm/[IMAGENAME].vmx nogui

You could also add /Applications/VMware Fusion.app/Contents/Library to your $PATH or create an alias to have easier access to the vmrun command.

You can find more info on the vmrun command in this PDF. While a bit out-dated, it should still contain relevant information on how to start and stop your server.

If you are interested in running headless Linux servers for your development environment etc, I can also highly recommend to use VirtualBox instead. It is free, has extensive command-line support, and while running headless VMs Fusion loses most if its advantages (seamless GUI integration) over VirtualBox anyway. What's more, tools like Vagrant can even facilitate running these environments to a much greater extent. With the addition of a paid add-on ("provider"), Vagrant can control VMWare as well as VirtualBox for you3.

An additional way, you can start up the VMs you want and then force quit VMware Fusion using Command+Option+Shift+Esc

The GUI quits but the VMs run in the background. To manage these VMs you can start VMware fusion again as usual and it will show you what's currently running.