Long-term photometric measurements of Neptune show variations of brightness over half a century. Seasonal change in Neptune's atmosphere may partially explain a general rise in the long-term light curve, but cannot explain its detailed variations. This leads us to consider the possibility of solar-driven changes, i.e., changes incurred by innate solar variability perhaps coupled with changing seasonal insolation. Although correlations between Neptune's brightness and Earth's temperature anomaly—and between Neptune and two models of solar variability—are visually compelling, at this time they are not statistically significant due to the limited degrees of freedom of the various time series. Nevertheless, the striking similarity of the temporal patterns of variation should not be ignored simply because of low formal statistical significance. If changing brightnesses and temperatures of two different planets are correlated, then some planetary climate changes may be due to variations in the solar system environment.