The last decade has seen many interesting applications of Question Answering (QA) technology. The Jeopardy! quiz show is certainly one of the most fascinating, from the viewpoints of both its broad domain and the complexity of its language. In this paper, we study kernel methods applied to syntactic/semantic structures for accurate classification of Jeopardy! definition questions. Our extensive empirical analysis shows that our classification models largely improve on classifiers based on word-language models. Such classifiers are also used in the state-of-the-art QA pipeline constituting Watson, the IBM Jeopardy! system. Our experiments measuring their impact on Watson show enhancements in QA accuracy and a consequent increase in the amount of money earned in game-based evaluation.