We show that the Gaussian con model of particles interacting via a penetrab
le repulsive Gaussian potential, first considered by Stillinger [J. Chem. P
hys. 65, 3968 (1976)], behaves as a weakly correlated "mean-field fluid'' o
ver a surprisingly wide density and temperature range. In the bulk, the str
ucture of the fluid phase is accurately described by the random phase appro
ximation for the direct correlation function, and by the more sophisticated
hypernetted chain integral equation. The resulting pressure deviates very
little from a simple mean-field-like quadratic form in the density, while t
he low density virial expansion turns out to have an extremely small radius
of convergence. Density profiles near a hard wall are also very accurately
described by the corresponding mean-field free-energy functional. The bina
ry version of the model exhibits a spinodal instability against demixing at
high densities. Possible implications for semidilute polymer solutions are
discussed.