We present new calculations of transit spectra of super-Earths that allow for atmospheres with arbitrary proportions of common molecular species and haze. We test this method with generic spectra, reproducing the expected systematics and absorption features, then apply it to the nearby super-Earth GJ 1214b, which has produced conflicting observational data, leaving the questions of a hydrogen-rich versus hydrogen-poor atmosphere and the water content of the atmosphere ambiguous. We present representative transit spectra for a range of classes of atmosphere models for GJ 1214b. Our analysis supports a hydrogen-rich atmosphere with a cloud or haze layer, although a hydrogen-poor model with <, ~10% water is not ruled out. Several classes of models are ruled out, however, including hydrogen-rich atmospheres with no haze, hydrogen-rich atmospheres with a haze of ~0.01 mu m tholin particles, and hydrogen-poor atmospheres with major sources of absorption other than water. We propose an observational test to distinguish hydrogen-rich from hydrogen-poor atmospheres. Finally, we provide a library of theoretical transit spectra for super-Earths with a broad range of parameters to facilitate future comparison with anticipated data.