How is sweating a pipe an example of capillary action? I learned how to sweat a pipe today from my father.  If you're not familiar with the process, this might help.
One thing that jumps out at me is this line (from the above link, as well as my father's explanation)

Solder, which melts at low temperatures, wicks into a joint by capillary action and bonds with copper at the molecular level.

This doesn't seem to be quite right to me.  I always thought of capillary action as something like putting a piece of paper vertically into a dye and watching the dye rise up the paper.  I also didn't think the solder bonded with the copper at the molecular level, just that it melted and filled in the gaps really well.  Wikipedia seems to agree with my definition of capillary action

Capillary action ... is the ability of a liquid to flow in narrow spaces without the assistance of, and in opposition to, external forces like gravity.

When sweating a pipe you place the solder above the pipe, letting it drip down (ie with the assistance of gravity) which makes it not capillary action... right?
Is there something I'm just not understanding here?
 A: The basis for capillary action is attraction between the liquid and the solid, based upon intermolecular or interatomic forces.
When the liquid needs to rise against gravity to increase wetted surface area, an equilibrium is reached.  However, capillary action does not need to be opposed to gravity.  Capillary action still takes place without gravity and then is not limited by an opposing force. 
A: When you were sweating the pipes, the solder was not only flowing with gravity.  It was also being drawn sideways, up, and around to fill the very small gap between the pipe and the fitting.  This is where the capillary action can be seen.
It is common, especially for small pipes (1/2 or 3/4 inch), to heat the entire joint and then apply solder to an edge on the "side" of the joint.  That is, neither the top nor the bottom, with respect to gravity.  When you can see a small band of solder around the entire joint, including the top, then you know that you've added enough.
To visualize what is happening, you could sweat a couple of pipes together, then cut through the joint the long way.  The solder will have filled the gap everywhere the fitting overlapped the pipe. That's why it's important to seat the pipe deep into the fitting.  The entire connection gets soldered, not just the outer seam.
A: Molten solder has a low contact angle on (clean) copper. So if you looked at a cross section of the pipe joint as the solder was flowing in you'd see something like:

The solder is drawn into the joint in exactly the same way as water rises in a capillary tube. Both are correctly described as capillary action.
A: Since you need to use flux on the pipe first the flux "primes" the connection so that when you heat the fitting and the flux burns off the solder is pulled into the joint to replace it.
