Graphene is a one-atom thick lattice of carbon atoms. It's super-capacitive, electrically conductive, biodegradable, 200 times stronger than steel, can take pretty much any shape, and is ultralight.
It's been theorized to help clean up nuclear waste, easily filter the salt from seawater, could make ridiculous headphones, is biocompatible -- meaning you can hook it right to biological cells, help make space elevators a reality, create flexible computers, unbreakable phone screens, and create the base for new supercomputers!
The biggest reason we aren't using graphene for everything yet is that it's very difficult to make in large quantities, but scientists are figuring out better and cheaper ways to produce it!
University of Manchester: The Story of Graphene
ABC: Scientists cook up material 200 times stronger than steel out of soybean oil
Phys.org: Physicists patent detonation technique to mass-produce graphene