Extrasolar super-Earths (1–10 M⊕) are likely to exist with a wide range of atmospheres. Some super-Earths may be able to retain massive hydrogen-rich atmospheres. Others might never accumulate hydrogen or experience significant escape of lightweight elements, resulting in atmospheres more like those of the terrestrial planets in our solar system. We examine how an observer could differentiate between hydrogen-rich and hydrogen- poor atmospheres by modeling super-Earth emission and transmission spectra, and we find that discrimination is possible by observing the transmission spectrum alone. An Earth-like atmosphere, composed of mostly heavy elements and molecules, will have a very weak transmission signal due to its small atmospheric scale height (since the scale height is inversely proportional to molecular weight). However, a large hydrogen-rich atmosphere reveals a relatively large transmission signal. The super-Earth emission spectrum can additionally constrain the atmospheric composition and temperature structure. Super-Earths with massive hydrogen atmospheres will reveal strong spectral features due to water, whereas those that have lost most of their hydrogen (and have no liquid ocean) will be marked by CO(2) features and a lack of H(2)O. We apply our study specifically to the low-mass planet orbiting an M star, Gl 581(c) (Msini = 5M⊕ ), although our conclusions are relevant for super-Earths in general. The ability to distinguish hydrogen-rich atmospheres might be essential for interpreting mass and radius observations of planets in the transition between rocky super-Earths and Neptune-like planets.