This sort of thing has been done many times on many TV shows and, I'm sure, science conventions. For instance, the Mythbusters, in their challenge to create device to help them climb up an air shaft, came up with two different ways to do it. One of them used electromagnets, and the other one used a vacuum system. While these worked (more or less), they weren't exactly slick. They were very large contraptions, needing to be attached to their backs. It's also been done using small vacuum cleaners, which I believe is a different technique to the above mentioned vacuum system used in the Mythbusters.
But anyway, I'm not going to use any of those techniques. The way I'm going to do it is from a show called Prototype This, which was an utterly brilliant show. To put very simply, they stuck a whole bunch of small fish hooks on two square boards with handles. That might sound a bit odd, but it works. Because the walls outside are rough, there are lots of very tiny bumps and ridges etc. which are all things the hooks can cling on to. True, one fish hook won't create that much resistance, but when you've got hundreds, it's a very different story. Each individual hook is a contact point, so when you've got a hundred contact points, you get a considerable amount of grip. Enough to hold the weight of someone, if you've got enough.
Here's the video of Prototype This doing it, in case you're interested: