For example when you build a circuit you have the board and the components between them is air.
Is there a clay like material that will act like air does?
Application: you could bundle simple circuits into a ball, attach adhesive to the outside and throw them at things (LED throwie)
If you want something like clay, what's wrong with clay? Just check it to make sure it's not conductive. I think you'd have more difficulty finding conductive clay than non-conductive...
Here's Elmer's Tac 'N Stik, which is probably more like what you want:
Also, here are instructions for cooking up insulating dough and conductive dough.
There are plenty of things out there that you could use as a conformal coating to insulate the circuit (just search digikey). As far as getting something sticky on the outside for use in throwies I would do that as a separate step once the circuit is insulated so you have more options and you can be more creative.
We use this pink stuff as a conformal coating. It is removable, which is great if you messed up and need to redo it.
EDIT: We've discovered that when the pink stuff is exposed to temperature changes in a vehicular environment, it can crack and moisture gets through and can cause damage to the board. You'll want to use something else (probably something that isn't totally hard) if you're project is used outside and/or on a vehicle.
Kapton tape is often used to cover and insulate circuits.
I've worked with circuits potted in wax. They were in a housing filled with wax, but you could use something like a milk carton and cut it away when the wax has cooled. The neat thing about potting with wax is that you can solder right through it.
There are also soft epoxy materials for electronic assemblies.
IIRC Epoxy Technologies (http://www.epotek.com) makes soft epoxy.
Try some polycaprolactone, its a low temperature melting plastic.
http://www.shapelock.com/page2.html
Never used it before, but from the looks of things you should be able to melt it in an oven and handle it with your hands to mould it into something.
I would second some of the epoxy resins.
You can really easily mix some of the stuff up, and coat your electronics in it.
You can create a mold to shape the epoxy out of wax. Make the final shape out of balsa wood or something (called the pattern), then melt some wax and push the pattern into the wax until the wax solidifies. Then place your electronics in the wax mold, then pour in the epoxy. You may want to brush on the epoxy to make sure you got it in all the right places and then put it with the rest of your epoxy. And since epoxy doesn't stick to wax, you just pull it straight out!
Silicone, like Dragon Skin from Smooth-On, works great. It's expensive though. And if you don't want it to cure with tiny bubbles in it, you need to use a vacuum chamber (I have access to one at my university).
The wax, epoxy, and clay answers above might work, but if you want to have something tested with electronics, you want potting compound. 3M Scotch-Weld DP270 (datasheet) and MG Chemicals' 832 series (different datasheets for color, strength, viscosity, hardness, etc.) are both popular examples. See the MG Chemicals appnote here [pdf] for a description of the potting and conformal coat processes.
Conformal coat is almost what you want: It insulates, but it doesn't provide the structure you want. It's a very thin coating (Like paint, but it's usually clear) that provides a high dielectric between the components and the air. Techspray, Humiseal, Loctite, MG Chemicals, and Chemtronics all manufacture it.
The other option is hot glue. Every stick I've used is nonconductive. Not sure how well it would work to make a ball, but it's worth a shot.
