Safe for you or safe for the PC?
If you are in an older residence with old wiring and outlets, you should connect the adapter's* ground wire to some grounded metal in the residence. Like a water pipe or ground rod.
*I presume by adapter you are using a 3 prong to 2 prong like this:
http://i.stack.imgur.com/993s9.gif
If your outlet box is grounded, you can connect the ground wire directly to the screw holding the outlet cover on.