In this paper, we derive the exact average symbol error probability (SEP) of M-ary phase-shift keying and quadrature amplitude modulation signals over Stacy fading channels. The Stacy fading is modelled by a three-parameter generalized gamma or physically α-µ fading distribution, spanning a wide range of small-scale fading such as Rayleigh, Nakagami-m, and Weibull fading. The average SEP is generally expressed in terms of (generalized) Fox's H-functions, which particularizes to the previously known results for some special cases. We further analyze the diversity order achieved by orthogonal space-time block codes in multiple-input multiple-output (MIMO) Stacy fading channels.