Have a look at the WikiPedia, where the issue is quite nicely explained:
http://en.wikipedia.org/wiki/Coulomb's_law
There, indeed they also call the constant, Coulomb's constant. I do not know, which convention of units Coulomb historically used, but I guess it's the static Coulomb, which has become part of the Gaussian system of measures, i.e., it defines the electric charge unit by Coulomb's Law in the form
|\vec{F}_{\text{estat}}|=\frac{q_1 q_2}{r^2}.
This is no longer the most natural definition since nowadays, on the most fundamental level, we understand the electromagnetic field as defined by the relativistically covariant Lagrangian,
\mathscr{L}=-\frac{1}{4} F_{\mu \nu} F^{\mu \nu} + \frac{1}{c} j_{\mu} A^{\mu}.
Here F_{\mu \nu}=\partial_{\mu} A_{\nu}-\partial_{\nu} A_{\mu} is Faraday's tensor in terms of the electromagnetic four-vector potential. It includes the electric and magnetic field components, and Maxwell's equation in this convention then read
\vec{\nabla} \cdot \vec{E}=\rho, \quad \vec{\nabla} \times \vec{B}-\frac{1}{c} \frac{\partial \vec{E}}{\partial t}=\frac{1}{c} \vec{j}.
The constraints that lead to the derivability of the electromagnetic field components from a vector potential, which read in the three-dimensional form
\vec{E}=-\frac{\partial \vec{A}}{c \partial t}-\vec{\nabla A^0}, \quad \vec{B}=\vec{\nabla} \times \vec{A},
are given by the inhomogeneous Maxwell equations,
\vec{\nabla} \times \vec{E}+\frac{1}{c} \frac{\partial \vec{B}}{\partial t}=0, \quad \vec{\nabla} \cdot \vec{B}=0.
In this interpretation the Coulomb Law reads
|\vec{F}_{\text{estat}}|=\frac{q_1 q_2}{4 \pi r^2}.
This is close to the Gaussian units but here the factor 4 \pi appears in the solution of Maxwell's eqs. and not in the eqs. themselves. This is the Heaviside-Lorentz system of units and used in theoretical high-energy physics.
The SI is invented for everyday use in electrical engineering and experimental physics. For theoretical physics in the relativistically covariant formulation it's a bit inconvenient, but of course the physics doesn't change with the change of units.