We present three-dimensional atmospheric circulation models of GJ 1214b, a 2.7 Earth-radius, 6.5 Earth-mass super Earth detected by the MEarth survey. Here we explore the planet's circulation as a function of atmospheric metallicity and atmospheric composition, modeling atmospheres with a low mean molecular weight (MMW; i.e., H2-dominated) and a high MMW (i.e., water- and CO2-dominated). We find that atmospheres with a low MMW have strong day-night temperature variations at pressures above the infrared photosphere that lead to equatorial superrotation. For these atmospheres, the enhancement of atmospheric opacities with increasing metallicity lead to shallower atmospheric heating, larger day-night temperature variations, and hence stronger superrotation. In comparison, atmospheres with a high MMW have larger day-night and equator-to-pole temperature variations than low MMW atmospheres, but differences in opacity structure and energy budget lead to differences in jet structure. The circulation of a water-dominated atmosphere is dominated by equatorial superrotation, while the circulation of a CO2-dominated atmosphere is instead dominated by high-latitude jets. By comparing emergent flux spectra and light curves for 50× solar and water-dominated compositions, we show that observations in emission can break the degeneracy in determining the atmospheric composition of GJ 1214b. The variation in opacity with wavelength for the water-dominated atmosphere leads to large phase variations within water bands and small phase variations outside of water bands. The 50× solar atmosphere, however, yields small variations within water bands and large phase variations at other characteristic wavelengths. These observations would be much less sensitive to clouds, condensates, and hazes than transit observations. © 2014. The American Astronomical Society. All rights reserved..