This is an interesting concept so I would give them a try at least once. BUT, they seem to have a lot of limitations that I don't like, for example not being able to adjust the pressure, the way they mount to the rim and it sounds really hard to remove.
From their website:
What are these tires made of?
Microcell urethane. That's the kind of material now used to make automobile dashboards, some seat cushions, and some vibration-dampening devices. We use a proprietary version of microcell urethane that's not typically available to other industries, and we make it up with a specific formula.
What puts the air bubbles in an Air Free tire?
It's a complicated and exacting process, like making really difficult bread. It requires several steps, and conditions have to be just right. You know how, even if humidity is wrong, bread won't rise right? The same kind of thing happens when you make microcell urethane. The bubbles are formed during an irreversible chemical reaction, which happens when you put the two components together. The first compound is isocyanate; the second one is proprietary, which means we can't tell you, but there could be many things in there: little bits of rubber, plastic, ball bearings. Mix the isocyanate with the secret stuff, and one of the byproducts is carbon dioxide. If you put the mixture in a mold, you'll trap a certain amount of the CO-2 in the foam.
So is an Air Free tire full of air, like a rubber tire? Or is it solid?
An Air Free tire has about 1/3 the air that would be in the same size tire if it were made out of rubber. So they're only 2/3 solid. They're full of little encapsulated bubbles. They're made of foam that is light and fluffy, like a souffli. It's like the process of making a difficult bread, but you end up with a souffli.
It also seems like they have done some testing on them too: http://www.airfreetires.com/Technical/default.asp