Slashdot linked up this PhysOrg article detailing the creation of the very first "nano-fabric":

The team led by Professor Andre Geim at The University of Manchester, has succeeded in extracting individual planes of carbon atoms from graphite crystals ... The resulting atomic sheet is stable, highly flexible and strong and remarkably conductive. The nanofabric belongs to the family of fullerene molecules, which were discovered during the last two decades, but is the first two-dimensional fullerene.

Yup, a sheet of fabric exactly one atom thick. There are immediate applications in computers and other eletronics, and who knows what else could be on the horizon. The article mentions this stuff has essentially the same properties as nanotubes, and they're talking about making a space elevator out of those. Right now they're only working with sheets a few microns across, but there's no phsycial limit to how big a sheet can be. It's just a matter of figuring out how to do it.