Original solid rubber tires in the 19th century gave a hard, bumpy ride. The invention of the pneumatic tire meant that the harshness of the old-style cobbled road could be evened out to give a pleasant 'floating' journey. It was this very quality of pneumatic tires that boosted the adoption of 'horseless carriages' and saw the rise of motor cars as our preferred mode of transport....
The tire absorbs a lot of the bumps and pot holes as well as the suspension, if they were solid rubber it would be a rough ride! They also help with traction and hold the road in curves, where a solid tire would be more apt to slide in higher speeds and spin more do to lack of traction
So the tire absorbs most of the bumps and potholes in the road helping the shocks. If the tire was made from solid rubber you would have worse handling and traction because tires with softer compounds tend to handle better on most surfaces
Solid rubber tires would give a bone jarring bumpy ride eventually blessing you with premature spondylitis. It would even wear out the suspension much more sooner than with air filled pneumatic tires. These are so much more comfortable and grip the road better too. My source - http://www.automotix.net/info.html