This article presents and discusses a critical compilation of accurate, fundamental determinations of stellar masses and radii. We have identified 95 detached binary systems containing 190 stars (94 eclipsing systems, and alpha Centauri) that satisfy our criterion that the mass and radius of both stars be known within errors of +/-3% accuracy or better. All of them are non-interacting systems, and so the stars should have evolved as if they were single. This sample more than doubles that of the earlier similar review by Andersen (Astron. Astrophys. Rev. 3:91-126, 1991), extends the mass range at both ends and, for the first time, includes an extragalactic binary. In every case, we have examined the original data and recomputed the stellar parameters with a consistent set of assumptions and physical constants.