Out of nowhere during one of my medium paced runs, I developed a pain in the outside portion of my right foot which got bad enough that I had to stop running. It's been nearly 24 hours, and walking is difficult due to pain.

I've never had a problem here before. There was no sudden pain, just a gradual build up.

Any clues on why this happened?

If you run all the time you could have runners foot (I think that is what it is called)
They say it is from your feet hitting the concrete hard over 800 times per mile. Between your weight and the impact on the ground it is hard on your feet.

running foot injuries - plantar fasciitis (http://www.pponline.co.uk/encyc/0180.htm)

Foot Problems In Runners (http://ezinearticles.com/?Foot-Problems-In-Runners&id=462082)

My ex husband developed that after he had been running for a number of months. He saw an podiatrist and was given some orthotics, which evened out his foot. Not saying that this is what is the matter with you, but you should see your doctor, at the very least. In running, the pavement is not always even (unless you are only running on an indoor track).

Please see your doctor and then go from there. Good luck.