We've heard of airless tires before seeing this photo, but those were for cars. These airless tires are for bikes, and you can only find them overseas. China uses them on a lot of their bikes, and they're basically made out of really tough foam. The foam tires have a bunch of air pockets in them, making the tires pretty shock-absorbent while also eliminating the possibility of having a flat tire.
As stated above, a lot of tire manufacturers are testing similar technologies for use on vehicles, so it's possible something like this could become a reality in the U.S. sooner rather than later.