craigb
I took part in a Guiness Book of World Records attempt for solving a Rubik's cube back in the early 80's. We had to solve five cubes (because some solutions require extra steps and you really can't know in advance). They take the average time of all five. I came in around 39 seconds but wasn't even a finalist.
All of the weird solutions you see like blind-folded or one-handed or, probably, the guy above are all BS. They start with solved cubes, then mess them up and play the result backwards. The better ones all add something like over-dubbing talking or someone walking backwards to help add to the illusion.
It was worked out that every Rubik's cube state can be solved in 20 moves or less. The algorithms have been refined over the years to achieve this minimum, which is why people are now solving it in 9 seconds and suchlike.
The book I had as a kid contained algorithms which were sometimes as long as 10-15 moves, so it wasn't exactly an efficient solution. Today's solutions contain more algorithms (presumably because they achieve stuff like moving numerous squares at once) so there's a lot more to memorize, but once you have that down it's just a matter of having the right dexterity.
The juggling video isn't played backwards by the way - you can see people walking and cycling in the correct direction in the background.
And here's a 7 year old kid solving the cube blindfolded at a competition - definitely not played backwards
Some people have extraordinary memories. Some people have an extraordinary spatial awareness. And then some people have both together. I think these are the ones who are doing these crazy cube feats.
Speaking of which, here's a guy solving a frigging 13x13 cube. It's a time lapse video over a couple of hours, and I don't think anyone's going to be solving one of these blindfolded in a hurry, but still, what an amazing achievement.