We might have airless tires. It's an idea that's been around almost as long as pneumatic tires. Certainly we could save a lot of weight, if only by eliminating the dead weight of the spare in the trunk.
Link to the Wikipedia page on the "Tweel:"
Tweel - Wikipedia, the free encyclopedia I've seen a couple of other concepts.
I recently saw something that more or less did away not with the pneumatic tire, but the separate suspension, the so-called "Loopwheel." It adds a lot of rotating mass but I wonder how much mass on the vehicle it could eliminate. In a two-wheel application like a bike or motorcycle it works because the wheel doesn't get exposed to much in the way of off-axis stresses, but in a car it might not hold up.