As you may be aware, in 2010, the Nobel Prize for Physics was awarded to Geim and Novoselov for their work with graphene. Wired already did a nice little piece on why it won the Nobel Prize, but they focused more on the possible applications of the material, rather than it's already awesome properties and history.
Graphene may be the first Nobel Prize awarded made possible by Scotch tape. Single layers of graphene were first separated by peeling tape off of a block of high-purity graphite. Graphene sheets are effectively two-dimensional, and within the plane of the sheet, are the strongest material ever tested. They also have remarkably high electron and hole mobility, making them ideal for many electronics applications.
So what is graphene being used in so far? Researchers at the University of Technology Sydney have figured out how to make a paper out of it. It's been used as a transparent anode in organic LEDs and organic photovoltaics. It's little sister, graphene oxide (GO), on the other hand, is a little more practical. It kills E. coli with surprising efficiency. It has also been used as reinforcement for epoxy composites. With as little as 0.125 weight % GO, the fracture toughness of the composite (i.e., how hard it is to start and propagate a crack) increased by 65%. To get equivalent improvements with carbon nanotubes, it took roughly 3%, and graphene oxide is much cheaper to produce.
Basically, it's pretty darn spiffy.