The earliest timekeepping devices were probably shadow clocks. A vertical gnomen erected to cast a shadow as the sun moves. The problem with ancient shadow clocks were that they did not move through the same angle per hour each day. In the summer the angle distance between noon and 3 pm was different than in the winter. To resolve this difference the ancients resorted to cutting hemi-spherical depressions in the face of the sun-dial and making markings for time in several different seasons. It seems that Ptolemy may have known that this could be corrected by pointing the gnomen in the correct angle (the angle of latitude for the dial) but this idea was not put into common practice until the Islamic mathematicians of the Middle Ages made some advances in spherical geometry. Sundials can also be mounted vertically as seen in this 1749 dial I photographed in the Cathedral Close at Salisbury Cathedral.
The dial was actually erected three years before the creation of the Gregorian calendar. The lines drawn across the face mark the sun's path at different seasons of the year. One of the characteristics of vertically mounted sundials (in the northern hemishphere) is that the shadow moves counter-clockwise or in a mathematically positive rotation. In the Basilica di Santa Maria del Fiore (this is the famous one that has the dome by Brunelleschi) in Florence there is an unusual clock dating to the 1400's by Paulo Uccello. The clock not only rotates in a positive (anti-clockwise) direction, it is a 24 hour clock. This may be the oldest mechanical clock in the world to meet both those conditions. I have not seen another major clockwork with both conditions, and would love to hear from anyone who knows of others.
The clock is one-handed, showing only the hour. Originally it used the 24 hours of the hora italica (Italian time), a period of time ending with sunset at 24 hours, which was used until about the 18th century. The clock now shows the standard time of the region.
There is another much more modern twenty-four hour clock at the Shephard Gate of the Royal Observatory at Greenwich. The Wikipedia article states, "The clock, an early example of an electric clock, was a slave mechanism controlled by electric pulses transmitted by a master clock inside the main building. The 'network' of master and slave clocks was constructed and installed by Charles Shepherd in 1852. The clock by the gate was probably the first to display Greenwich Mean Time to the public". Note that it moves in the standard clockwise or mathematically negative rotation.
I have come across several other 24 hour clocks, but none that go in a mathematically positive rotation, and no others as old as the one in Florence. There is one in Piazza San Marco in Venice that has midnight at the "three O'clock" position; probably also for liturgical times using the old Italian method of beginning and ending the day at sunset. The Wells Cathedral mechanical clock (now in the Museum of Science in London) is a 24-hour clock that really counts to twelve twice around the clock face. It also travels in a standard clockwise rotation.
If you are willing to overlook the flaw of negative rotation, you can download a 24 hour clock widgit from Yahoo Widgets.