Finite mixtures of the following ten families of univariate distributions are shown to be identifiable: logarithmic series, discrete rectangular, rectangular, first law of Laplace, noncentralX^{2}, logistic, generalized logistic, generalized hyperbolic-secant, inverse Gaussian, and random walk. A generalized version of a theorem given by Teicher is used to show that the finite mixtures of the following multivariate distributions are also identifiable: negative binomial, logarithmic series, Poisson, normal, inverse Gaussian, and random walk.