rusty monkey,
My house is 1960 (and in Greendale btw, so we're practically neighbors) and had all two prong outlets. I replaced every one with regular three prong and since the BX cable is grounded to the box, the screws holding in the receptacle provide a ground path. Buy one of those testers you plug into the receptacle and it will diagnose an open ground, reverse polarity, etc. etc. I also installed GFCIs in the bathrooms, garage, kitchen and outdoors. Everything is kosher as far as I can tell.
You can even double check the outlet by sticking an electrical tester (the one with the light) into the line side and touch one of the screws holding the receptacle (not the cover) and it should light up proving that current can travel to ground. Since this worked for me I did not pigtail a ground wire from the receptacle to the box.
Finally, my system is grounded to the water pipes. Just ensure that there are jumpers around stuff that does not conduct electricity!
ps GFCI outlets cost $12.00. Regular receptacles cost 29 cents or something like that