The original 12 hour clock was the mesopotamian/egyptian sundial. Here's an example. This was continued by the romans. The 24 hour system came about to account for the night hours, which was more useful the further from the Mediterranean. However, it was still divided into two cycles of twelve hours. The AM/PM notation came about because it's easiest to divide time based on when the sun is at its highest; this is reflected in the 'ante meridian'/'post meridian' phrases that form the AM/PM.

So, it's more of a question of when we were able to keep accurate enough time at night to be able to have 24 hours and switch FROM the 12 hour clock. The ancient egyptians and greeks both used water clocks, but i don't have any information available as to how they divided the time as it drained (if they did at all). The answer to that, of course, is the development of mechanical time pieces.

I remember the [Science museum in London] (http://www.sciencemuseum.org.uk/visitmuseum_old/galleries/time_measurement.aspx) has a splendid collection of various types of clocks. Including one that just divides up the daylight in 12 equal portions, no matter how long the day lasts. So you'd have shorter hours in the winter and longer in the Summer. Better hope all your friends use this clock too.

The first mechanical clock dates from the 14th century. And with that came the switch from 12 to 24 hours:

Mechanical clocks brought about a change in the way in which time was measured. Before the 14th century, the system of dividing a period of one day and one night into 24 equal hours was only used by astronomers. For most people, the periods of daylight and darkness were each divided into 12 "temporal hours", which varied in length throughout the year. This is convenient with sundials but the speed of a mechanical clock does not vary in this way. By the end of the 15th century, most people in Europe had switched to the modern system and the design of sundials had changed to use it as well."

So the mechanical clock I mentioned that divides the day into 12 sunlit equal portions is quite an anomaly!

btw, in the Medieval period (and before and after that) a day started in the evening. The evening was typically part of the following day. Hence the importance of "Christmas Eve" and the celebration of Saint Nicholas' birthday on Dec the 5th when his actual birthday is Dec 6th. I mention Medieval period because the last prayer of the day is at 7 in the evening. (and the first is at 2AM)

How we came to chose 12 as the beginning/end of a day I have no clue. 12 PM doesn't even sync with the highest point of the sun on a sundial (as far as I'm aware. It usually is at half past 12 or 1 o'clock even).

Follow up: Is 12 hour time even that common outside English-speaking countries? I never encountered it before moving to the USA (from Iceland).