The Sun has a steady 11-year cycle in magnetic activity most well-known by the rising and falling in the occurrence of dark sunspots on the solar disk in visible bandpasses. The 11-year cycle is also manifest in the variations of emission in the Ca II H & K line cores, due to non-thermal (i.e. magnetic) heating in the lower chromosphere. The large variation in Ca II H & K emission allows for study of the patterns of long-term variability in other stars thanks to synoptic monitoring with the Mount Wilson Observatory HK photometers (1966-2003) and Lowell Observatory Solar-Stellar Spectrograph (1994-present). Overlapping measurements for a set of 27 nearby solar-analog (spectral types G0-G5) stars were used to calibrate the two instruments and construct time series of magnetic activity up to 50 years in length. Precise properties of fundamental importance to the dynamo are available from Hipparcos, the Geneva-Copenhagen Survey, and CHARA interferometry. Using these long time series and measurements of fundamental properties, we do a comparative study of stellar "twins" to explore the sensitivity of the stellar dynamo to small changes to structure, rotation, and composition. We also compare this sample to the Sun and find hints that the regular periodic variability of the solar cycle may be rare among its nearest neighbors in parameter space.