A variety of terrestrial planets with different physical parameters and exotic atmospheres might plausibly exist outside our Solar System, waiting to be detected by the next generation of space-exploration missions. Some of these planets might transit their parent star. We present here the first study of atmospheric signatures of transiting Earth-size exoplanets. We focus on a limited number of significant examples, for which we discuss the detectability of some of the possible molecules present in their atmospheres, such as water, carbon dioxide, ozone or molecular oxygen. To this purpose, we developed a model to simulate transmission spectra of Earth-size exoplanets from the ultraviolet to the near infrared. According to our calculations, the signatures of planetary atmospheres represent an absorption of a few parts-per-million (ppm) in the stellar flux. The atmospheres of a few Earth-like planets can be detected with a 30-40m telescope. The detection of the extensive atmospheres of tens of small satellites of giant exoplanets and hundreds of hypothetical ocean-planets can be achieved with 20-30m and 10-20m instruments, respectively, provided all these planets are frequent and they are efficiently surveyed. We also found that planets around K stars are favored, mainly because these stars are more numerous and they are smaller compared to G or F stars. While not addressed in this study, limitations might come from the stellar photometric micro-variability.