That's a very deep question, one of the core questions for physics. Usually, we modify it a little before tackling it. The value e=1.6*10^-19 Coulombs
has a number that depends entirely on the choice of units, which just come from historical accidents. So when we start wondering about the values of things, we first convert them to unitless ratios. For e, we then wonder why the 'fine structure constant', 2πe2
/hc, takes on its value of roughly 1/137. (h is Planck's constant, c is the speed of light.)
There are many other dimensionless ratios: ratios of masses of particles, strength of the short-range interaction between quarks (expressed like we did for e), the number of spatial dimensions of our universe, the ratio of the background 'dark energy density to the critical energy density, etc. All told there are a couple of dozen or so such numbers.
Currently we have no explanation for these numbers. The best framework to look for an explanation is string theory, an attempt to find a unifying theory for all the fundamental physical effects. Current work indicates that there are probably a huge number of fairly stable solutions to the underlying string theory, each giving rise to a different set of physical constants for our 'ordinary' physics.
I believe the best guess about why we have our particular constants is that nature has domains in which each of the solutions occurs. However, only very special values of the constants support a universe with chemistry, which seems to be a prerequisite for life. In the dead universes nobody's asking why the values are what they are.
There's a nice book on this, called 'The Cosmic Landscape", by Lenny Susskind.
(published on 04/20/09)