We present an analysis of long-term photometric variability for nearby red dwarf stars at optical wavelengths. The sample consists of 264 M dwarfs south of decl.=+30 with V-K=3.96-9.16 and M_V_~~10-20, corresponding to spectral types M2V-M8V, most of which are within 25pc. The stars have been observed in the VRI filters for ~4-14yr at the CTIO/SMARTS 0.9m telescope. Of the 238 red dwarfs within 25pc, we find that only ~8% are photometrically variable by at least 20mmag (~2%) in the VRI bands. Only four stars have been found to vary by more than 50mmag, including GJ 1207 at 8.6pc, which experienced a single extraordinary flare, and GJ 2006 A, TWA 8 A, and TWA 8 B, which are all young stars beyond 25pc linked to moving groups. We find that high variability at optical wavelengths over the long term can in fact be used to identify young stars. Overall, however, the fluxes of most red dwarfs at optical wavelengths are steady to a few percent over the long term. The low overall rate of photometric variability for red dwarfs is consistent with results found in previous work on similar stars on shorter timescales, with the body of work indicating that most red dwarfs are only mildly variable. As expected, we find that the degree of photometric variability is greater in the V band than in the R or I bands, but we do not find any obvious trends in variability over the long term with red dwarf luminosity or temperature. We highlight 17 stars that show long-term changes in brightness, sometimes because of flaring activity or spots, and sometimes because of stellar cycles similar to our Sun's solar cycle. Remarkably, two targets show brightnesses that monotonically increase (G 169-029) or decrease (WT 460AB) by several percent over a decade. We also provide long-term variability measurements for seven M dwarfs within 25pc that host exoplanets, none of which vary by more than 20mmag. Both as a population, and for the specific red dwarfs with exoplanets observed here, photometric variability is therefore often not a concern for planetary environments, at least at the optical wavelengths where they emit much of their light.