Tonight I installed VMware Player on my Windows machine to experiment with a few things. After getting it installed, I downloaded the latest Ubuntu image and created a virtual machine with it. Everything went pretty smoothly.
VMware, by default, intercepts Ctrl-Alt to exit full-screen mode. Switching virtual workspaces in the windows manager in the new Ubuntu machine uses Ctrl-Alt-<Arrow key>, and the VMware keystroke interfered with left and right. It took a while to find it, but Ctrl-Alt-Space followed by Ctrl-Alt-Right, for example, accomplishes the switch, but this is inconvenient. Remapping the keystrokes that switch virtual workspaces is straightforward, but I am too accustomed to Ctrl-Alt-<Arrow key> to do that.
I found how to change the VMware keystroke here. The sixth box on that page had what I needed and changed the VMware keystroke to Ctrl-Alt-Shift. I only used the first three lines because the second block has some syntax error in my version of the Player.