It's a good thing to keep up on your tires, their condition, age, proper air pressure (also good for gas mileage), and to replace when they need it. But keep in mind a car with worn suspension/steering components, etc, can cause premature tire failure. Just because your tires are within an acceptable age range doesn't mean you are off the hook. Just be reasonable and diligent about your car maintenance overall.

Around here about 7 years or so ago a cyclist died when a pickup truck tire blew and the truck swerved into him.