We present the results of a study of interstellar extinction in the visible to near-infrared, based on a photometric study of 154 highly obscured OB stars in the southern Milky Way. Absolute visual extinctions (A(V)) of individual stars are deduced by three distinct methods, with extrapolation to zero frequency based on (1) the van de Hulst theoretical curve 15, (2) the empirical formula of Cardelli, Clayton, & Mathis, and (3) the power law of Martin & Whittet. Results agree to within 3%, and we conclude that the relation A(V) = 1.1 E(V-K), based on the van de Hulst curve, provides a reliable and straightforward way to estimate A(V) for individual stars. Results lie in the range 2 mag < A(V) < 6 mag for stars in our sample. Our catalog of highly reddened stars provides a potentially valuable source list for future studies of interstellar phenomena within 10 kpc of the Sun, such as gas-phase atomic and molecular abundances, cloud kinematics, polarization, and the morphology of the Galactic magnetic field, as well as interstellar extinction. In this paper we use the data to refine various parameters which characterize the extinction law. We derive a mean extinction curve, yielding a ratio of total to selective extinction R(V) = A(V)/E(B-V) = 3.08 +/- 0.05. Values for individual stars lie in the range 2.5-4.7. Stars with R(V) substantially greater than the mean value tend to lie relatively close to the Sun, suggesting that their extinctions may be dominated by dust in local dark clouds. The mean value of R(V) for stars beyond 2 kpc is 2.97 +/- 0.03. We confirm previous results which suggest that extinction curves converge to a single functional form in the infrared (lambda > 0.90 mu m), well described by a power law of index 1.73 +/- 0.04 and further characterized by a color excess ratio E(J-H)/E(H-K) similar or equal to 1.64. We also show that visual extinctions may, in principle, be estimated purely from measurements in the infrared using the relation A(V) = rE(J-K), where r similar to 1.87/(0.65 - R(V)(-1)). This result may be applied to the problem of determining A(V) for highly obscured objects lacking optical counterparts in regions where R(V) is known.