I know a bit about electrical work, so here goes:
GOOD GOD DON'T BREAK OFF THE GROUNDING PIN. As said before, get one of those adapters.
The instructions for your surge protector are technically correct - you're not REALLY supposed to even use those adapters, as you will likely still not have any grounding going to your surge protector.
I said LIKELY, because those adapters usually come with a little tab that you can screw into the faceplate of your outlet, which MIGHT be (although it probably isn't) grounded.
Do you NEED grounded outlets? Weeellllll...yes and no. IN THEORY, as long as you don't have any problems or shorts with your wiring, you don't need grounding. Ground just supplies a safe path for the current to go to if there is a short - if you do have a short with an ungrounded outlet, there is no "safe path", and either you or your equipment can get cooked.
My honest advice: get an electrician to wire in a grounded outlet.