Revisiting the now de facto standard Stanford dependency representation, we propose an improved taxonomy to capture grammatical relations across languages, including morphologically rich ones. We suggest a two-layered taxonomy: a set of broadly attested universal grammatical relations, to which language-specific relations can be added. We emphasize the lexicalist stance of the Stanford Dependencies, which leads to a particular, partially new treatment of compounding, prepositions, and morphology. We show how existing dependency schemes for several languages map onto the universal taxonomy proposed here and close with consideration of practical implications of dependency representation choices for NLP applications, in particular parsing.