Through the McDonald Observatory M Dwarf Planet Search, we have acquired nearly 3000 high-resolution spectra of 93 late-type (K5-M5) stars over more than a decade using the High Resolution Spectrograph on the Hobby-Eberly Telescope. This sample provides a unique opportunity to investigate the occurrence of long-term stellar activity cycles for low-mass stars. In this paper, we examine the stellar activity of our targets as reflected in the H{alpha} feature. We have identified periodic signals for six stars, with periods ranging from days to more than 10 years, and find long-term trends for seven others. Stellar cycles with P>=1 year are present for at least 5% of our targets. Additionally, we present an analysis of the time-averaged activity levels of our sample, and search for correlations with other stellar properties. In particular, we find that more massive, earlier type (M0-M2) stars tend to be more active than later type dwarfs. Furthermore, high-metallicity stars tend to be more active at a given stellar mass. We also evaluate H{alpha} variability as a tracer of activity-induced radial velocity (RV) variation. For the M dwarf GJ 1170, H{alpha} variation reveals stellar activity patterns matching those seen in the RVs, mimicking the signal of a giant planet, and we find evidence that the previously identified stellar activity cycle of GJ 581 may be responsible for the recently retracted planet f in that system. In general, though, we find that H{alpha} is not frequently correlated with RV at the precision (typically 6-7m/s) of our measurements.