The older Explorers don't really roll over any easier than any other sUV, there were just so many of them made and so many people driving them like cars, that they did crazy things and rolled them over. Running the tires at low pressure probably didn't help.
The original factory sticker for air pressure advises 26 psi..which was WAY too low, but was probably so it had a nicer ride..or felt like it did. Later on after the Firestone tire fiasco, Ford issued stickers to put over the original ones that advised 30-32 psi.
Since most passenger car tires (which is usually what winds up on Explorers) are rated for 35 psi max, 32 is probably what you want for the best mileage and wear, though it will depend on the tire. Some tires might ride nice and wear better at 35, others will need to be at 30 psi and will still ride a little rough.
Properly inflated tires will reduce the risk of a blowout (underinflated tires build up more heat), will allow the Explorer to corner better (less lean in corners), and let the other systems (brakes, suspension, etc. work their best) and is probably the easiest thing you can do to keep it safe to drive, other than of course driving it safely to begin with.
