++ By the time you feel soft to you they've likely gone down too much to ride without risking more flats or even rim damage. Also, "stone-like stiffness is not the measure to use when you pump them up. Check them with a pressure gauge (not with the one on the pump, as some of the air in the tire will go into the pump and give a too-low reading).

When you pump them go by the max pressure on the tire as a guideline. Check Sheldon's site for recommendations (much better than getting a random selection here. I would not ride with more than 10% less than whatever pressure you decide works for you.

p.s. For that matter your initial question would have been answered by his site as well.