© 2015. The American Astronomical Society. All rights reserved. Planets larger than Earth and smaller than Neptune are some of the most numerous in the galaxy, but observational efforts to understand this population have proved challenging because optically thick clouds or hazes at high altitudes obscure molecular features. We present models of super Earths that include thick clouds and hazes and predict their transmission, thermal emission, and reflected light spectra. Very thick, lofted clouds of salts or sulfides in high metallicity (1000 solar) atmospheres create featureless transmission spectra in the near-infrared. Photochemical hazes with a range of particle sizes also create featureless transmission spectra at lower metallicities. Cloudy thermal emission spectra have muted features more like blackbodies, and hazy thermal emission spectra have emission features caused by an inversion layer at altitudes where the haze forms. Close analysis of reflected light from warm (∼400-800 K) planets can distinguish cloudy spectra, which have moderate albedos (0.05-0.20), from hazy models, which are very dark (0.0-0.03). Reflected light spectra of cold planets (∼200 K) accessible to a space-based visible light coronagraph will have high albedos and large molecular features that will allow them to be more easily characterized than the warmer transiting planets. We suggest a number of complementary observations to characterize this population of planets, including transmission spectra of hot (≳1000 K) targets, thermal emission spectra of warm targets using the James Webb Space Telescope, high spectral resolution (R∼105) observations of cloudy targets, and reflected light spectral observations of directly imaged cold targets. Despite the dearth of features observed in super Earth transmission spectra to date, different observations will provide rich diagnostics of their atmospheres.