Why doesn't a fly fall off the wall?

See http://www.sciencephoto.com/media/100845/enlarge for an absolutely awesome picture of a fly's foot. It has two claws that can grip any irregularities. For smooth surfaces like glass it has a pad covered in tiny hairs, and each hair is coated in tiny oil drops. The capillary attraction of the oil drops holds the tiny hairs, and therefore the fly, to the surface.

To add to John's answer, scientists have an enlarged image of Spider's legs (up to $5\mu m$) whose smallest hairs are named setules. This make the spiders, a level up than flies or geckos... Also, These attractive (adhesive) forces in those setules can make the spiders capable of sticking to an overhead wall, just using a single paw..!

It should be noted that even small amounts of water could wash off this capillary attraction and it would flush away these tiny organisms 'cause these forces are only negligible..!

Reference: http://whyfiles.org/shorties/152sticky_spider/

Geckos use van der Waals forces: http://www.pnas.org/content/99/19.cover-expansion