Current research into spoken language translation (SLT),or speech-to-text translation, is often hampered by the lack of specific data resources for this task, as currently available SLT datasets are restricted to a limited set of language pairs. In this paper we present Europarl-ST, a novel multilingual SLT corpus containing paired audio-text samples for SLT from and into 6 European languages, for a total of 30 different translation directions. This corpus has been compiled using the debates held in the European Parliament in the period between 2008 and 2012. This paper describes the corpus creation process and presents a series of automatic speech recognition, machine translation and spoken language translation experiments that highlight the potential of this new resource. The corpus is released under a Creative Commons license and is freely accessible and downloadable.