In this paper, we present a comprehensive analysis of the outage probability for multiple-input multiple-output (MIMO) systems over spatially correlated Rayleigh fading channels. In our analysis, we assume that 1) the channel state information (CSI) is perfectly known at the receiver but not at the transmitter, 2) the spatial correlation is present at both ends of the wireless communications link, 3) the transmit and receive correlation matrices may or may not be full rank, and 4) the underlying channel is quasi-static fading. With these assumptions, we derive explicit bounds for the outage probability and show that the diversity order is simply the product of the rank of the transmit correlation matrix and the rank of the receive correlation matrix. We also derive an expression that accurately quantifies the degradation in the signal-to-noise ratio (SNR) due to the presence of correlation. We present several numerical examples that validate our analysis.