Well...here's my halfhearted crack at explaining the gecko foot thing, as I somewhat remember reading:
Gecko feet are a lot like hook-and-loop fasteners (velcro.) Without the hooks. And the loops are microscopic, and solid, so not really loops at all, but rather just little "papillae" or "nubs." Think of your tongue with longer, taller taste buds on a microscopic scale. Hey, gimme a break, I'm tryin' here! :P
The theory is that these eensy little flexible nubbins of gecko skin are the key element, thus efforts to reproduce gecko feet in the lab have focused on mimicking the tiny nubs. The research has confirmed that these are indeed what's working. Less certain is why. Speculation is that this is molecular interaction between the skin and the surface--something on the order of hydrogen bonding or such. Or perhaps friction. The little nubs may serve to drastically increase surface area, magnifying a weak little adhesive force dramatically, and/or perhaps allowing the force to be broken easily.
The reason this is so cool isn't so much the sticking (though the sticking is quite respectable) as it is the instant on/off nature of the sticking. Slap the foot down, it's stuck...no need for glue to set or cure, etc. To remove the foot, peel up one edge of it--comes off like it's not stuck at all. The little nubs each have a terribly weak adhesion, so peeling an edge up only pulls on a few at any given time--thus they let go like nothing happened. Pull on them all at once, however (by, say, climbing the walls) and they hold fast. Thus, you've got an adhesive that's instant on/easy off and totally reusable. Sort of like post-it notes, but infinitely better.
I love stuff like this, sci-fi stuff popping up for real. Even if I'm totally off in remembering what I've read on it, I don't care...it's just too cool.