It seems that some madman, and I say that with reverence as the world truly lacks a good dose of madness on a good day, has free climbed (I.E. ropeless) the Eiger.
He did it with a twist, however. He wore a parachute designed for BASE jumping. Traversing onto a north face route called "Deep Blue Sea" at a height sufficient for BASE jumping, he managed a successful send without needing the 'chute.
FreeBASEing the Eiger - Dean Potter Interviewed
I am not a good climber, nor a particularly accomplished one, but I frickin' love it and am always in awe of amazing performances. This is without a doubt one of the more amazing I've heard of.