VMware Workstation (Pro) for Windows hosts
The full screen toolbar can be completely hidden directly via the UI. On Windows, go to Edit > Preferences > Display and uncheck "Show toolbar edge when unpinned in full screen". (Doing so will write pref.fullscreen.toolbarPixels = "0" to your %APPDATA%\VMware\preferences.ini file.)
Entering "Exclusive Mode" also will completely hide the full screen toolbar. (Exclusive Mode additionally will force most keyboard shortcuts to go to the guest instead of allowing them to be intercepted by the host.)
VMware (Workstation) Player (and VMware Remote Console) for Windows hosts
Unfortunately, there is no UI to directly hide the full screen toolbar completely. You will need to:
Quit all running instances of Player.
Modify your preferences file directly and add the line:
pref.vmplayer.fullscreen.nobar = "TRUE"
The preferences file is located at %APPDATA%\VMware\preferences.ini. (%APPDATA% is an environment variable that typically expands to something like C:\Users\YOUR_USERNAME\AppData\Roaming.)
Restart Player.