What makes a material adhesive (or sticky)? I currently have a bandage on my arm that isn't sticking to me but definitely sticks to itself. It brought up the question: 
What makes a material sticky? What's happening on the molecular level? Why do some materials stick to some things better than to others?
 A: There are several different types of adhesion. As pointed out by Ryan S. :
Electrical, like when a balloon sticks to your head after a good rubbing. Chemical, like plastic cement will "melt" the plastic pieces to be bonded together. And the most common, physical, which is extremely hard to make an example of without a picture. Therefore, I give you a picture. 
What we have here, is paper. Normal paper. (Thanks for the picture Arstechnica!)

Glue, or other adhesive (like gum) can squeeze itself into the spaces between the fibers, and harden. The hardening while in an irregularly shaped form is what makes glue sticky. (That, and some amount of chemical bonding.)
I would think that in a case of a bandage, the electrical adhesion would be negligible. Probably most of the "stickiness" would come from the glue pressing into a crack/ around a hair etc. I would also guess that it would have a fair amount of chemical adhesion, but I would think that that would occur after the bandage had been worn for some time. 
Then again, the manufacturers have probably found a formula that gives an extremely "bond happy" substance.
http://en.wikipedia.org/wiki/Adhesive_bandage
A: Sorry, new to this forum! Adhesion works a few different ways (these are the most common):
Chemical bonds (super glue or tape)
Mechanically (think Legos or Velcro)
Electrically (think fabric softener sheet stuck to you pant leg)
As far as the bandage that won't stick to your arm: the chemical adhesive probably cannot hold onto the oils on your skin. Does that help?
