We derive general, unified expressions for the probability density function, cumulative distribution function, and mean SNR of generalized selection combining operating over multibranch, arbitrary, correlated, non-identical fading channels. The expressions are written in terms of the joint probability density function of the branch signals and allow for the equalgain and maximal-ratio methods in the combining stage. As an application example, we analyze the case of exponentially correlated Rayleigh channels. The analytical results are fully validated through Monte-Carlo simulations. In passing, new important expressions for the joint distribution and density of the order statistics of arbitrary correlated variates are also derived. Keywords— Arbitrary fading channels, generalized selection combining, order statistics.