Considering the practically important case of two transmit and an arbitrary number of receive antennas, we provide a simple closed-form expression for the asymptotic pairwise error probability (PEP) of space-time codes (STCs) in generalized fading including Rayleigh, Ricean, Nakagami-q, Nakagami-m, Weibull, and generalized-K fading. The presented analysis provides new insights into STC design and can be used to obtain tight asymptotic upper bounds for the bit, symbol, and frame error probabilities of arbitrary STCs.