The Fine Structure Constant, named alpha ( alpha=e2/hc ) is described in detail in write-up's by Oneiromancer and ugah174.

But alpha may not be as constant as what was once thought.
This is the suggestion made by a team of Australian physicists who published their findings in the journal Physical Review Letters's August 2001 issue.

It has always been thought that alpha was a dimensionless number roughly equivalent to 1/137 and this value plays a fundamental part in our understanding of electromagnetism.
A recent study led by John K. Webb of the University of New South Wales suggests that the value might have changed over the last 10 billion years by as much as 1 part in 100,000.

Using the Keck Telescope in Hawaii, the team compared the value of alpha some 12 billion years in the past to that of today.
This involved observing light from very old quasars passing through gaseous clouds on their way to Earth. In total 49 clouds were observed ranging between 5.5 billion and 11 billion light years distant. Each cloud that the light from the quasars passed through changed the spectrum image of the light based on the elemental composition of the clouds (in particular based on the presence of metallic ions in the clouds).
If alpha remained constant then the ions in the clouds should have absorbed parts of the light spectrum in the same way that ions on earth do today.
By comparing the composition of the light from the quasars to that of light on Earth the scientists could determine what changes to alpha had occured over the last 10 billion years.
According to the study it appears that alpha has grown over time.

If this is true, that fundamental constants can change or evolve over time, it would mean that many of the principles on which orthodox science is based will have to be revisited. But no-one is wiping the slate just yet.
The team members have been quick to point out that there is a 1 in 10,000 chance that a statistical error might be present in their findings and have called for another, internationally sponsored, independant measurement to verify of refute the findings of this experiment.

sources:
The Economist: 6 April 2002
The Quasar Absorption Line Fine Structure Experiment http://www.astro.psu.edu/users/cwc/fsc.html
News in Science http://www.abc.net.au/science/news/stories/s410048.htm
Space.com http://www.space.com/scienceastronomy/generalscience/constant_changing_010815.html