As more and more treebanks, i.e. syntactically annotated corpora, become available for a wide variety of languages, machine learning approaches to parsing gain interest as a means of developing parsers without having to repeat such labor-intensive and language-specific activities as grammar development for each new language. In this paper, we describe two different machine learning approaches to the CoNLL-X shared task on multi-lingual dependency parsing. First, we introduce a number of baselines that generate left-branching, right-branching or more complex trees. Next, we present two systems that were submitted to the shared task: 1) an approach that directly predicts all dependency relations in a single run over the input sentence, and 2) a cascade of phrase recognizers. We find that the first approach performs best and conclude with a detailed error analysis of its output for two of the thirteen languages in the task, Dutch and Spanish.