After a couple of hours trying to figure it out why every time I tried to log in to my Ubuntu VM using VMware Fusion on a mac the vm would crash and restart itself, I came up with a thread in the VMware Communities forum explaining the reason + possible solution for the problem.

Basically what happened was that the Ubuntu would start just as expected, but after logging in it would popup this message:
Screen Shot 2013-01-20 at 9.31.51 PM

Quoting their explanation:

…If you are running a mid-2012 MacBook Pro with the latest Apple updates, you’ll likely encounter crashes unless you disable 3D graphics: With your VM powered off, go into Virtual Machine > Settings, then choose Display, and turn off the Accelerate 3D Graphics option.
For others encountering the same problem: if you only run Windows VMs, you would also have the option of reverting to Fusion 5.0.1 to avoid this issue.

Indeed, after disabling 3D acceleration support everything came back to normal.