All tires have the ability to absorb shock from road imperfections such as cracks and potholes. Some tires are better at absorbing shock than others. Michelin advertises its line of passenger car tires as having the softest ride of the major tire brands in luxury passenger car applications. Goodyear, one of the oldest makers of car tires in the world, also makes tires that are designed to give comfortable rides. However, a softer ride usually means a softer rubber compound in the tire. This will normally mean a shorter lifespan for the tire. You will need to balance all-weather traction, tread life, cost and shock absorbing capability when looking for new tires.
For more info, see Finding the Right Aftermarket Tires for You