EDIT on 11/2/2013: POKE A HOLE AT THE TOP OF THE APEX!!! It took me a year to figure that out.
Is the cohesive force of water stronger than gravity? Answer: yes (look at water cling to the side of a glass). Therefore, capillary action will pull water uphill.
For an example, look at a tree. A tree is a slow motion fountain.
Or touch the end of a napkin into water and the water crawls up. That's capillary action. Also note how it filters certain heavier substances. So the design of the napkin (sponge) can extract discrete particles from the fluid.
Edited on 3/30/2010:
Capillary action in a small diameter tube can raise water several centimeters. If you were to bend the end of the tube over, the water would attempt to flow out, but the cohesion will be stronger than gravity. However, if you were to arrange many similar tubes together, the meniscus of each would touch and the hydrogen bonding of water would overcome the electrostatic charge to the tube and water can form a droplet large enough for gravity to overcome. That's nearly perpetual energy that concentrates the electrostatic energy in water. That's how water gets into a coconut. Similar to nature, capillary faucets engineer water to travel uphill.
Edited to add picture on 4/18/2010:
Edited to add picture on 1/11/2010:
Another design using the same principles (1/27/2010):