You don't have to be a superhero like Spider-Man to climb on walls. Researchers have developed "Gecko Gloves" that can help humans climb on glass walls.
It sounds interesting but it is way too slow. Plus you couldn't go up surfaces that weren't perfectly flat. I'd love to see some that would allow a person to climb up a rock wall.
That's pretty cool, looks slow for certain... but with refinement like you said, I could see entire suits being made from it so that you could virtually scale any surface. Eventually we'll make devices to fly us individually, climb walls like spider-man, or even the Japanese Robots that can perform nearly any task.