Run flats will harden the ride of the car a bit and will be very expensive. Just invest in a few items and some diligence and your fears will go away.

1) Maintain and inspect your tires REGULARLY, can't stress this enough!!!
2) Purchase a "GOOD" ANALOG tire gauge and keep it in your trunk!
3) Purchase a "GOOD" tire plug kit and keep it in your trunk!
4) Watch the road, avoid potholes, debris and curbs.