Most current cross-lingual transfer learning methods for Information Extraction (IE) have been applied to local sequence labeling tasks. To tackle more complex tasks such as event extraction, we need to transfer graph structures (event trigger linked to multiple arguments with various roles) across languages. We develop a novel share-and-transfer framework to reach this goal with three steps: (1) Convert each sentence in any language to language-universal graph structures; in this paper we explore two approaches based on universal dependency parses and fully-connected graphs, respectively. (2) Represent each node in these graph structures with a cross-lingual word embedding so that all sentences, regardless of language, can be represented within one shared semantic space. (3) Using this common semantic space, train event extractors on English training data and apply them to languages that do not have any event annotations. Experimental results on three languages (Spanish, Russian and Ukrainian) without any annotations show this framework achieves comparable performance to a state-of-the-art supervised model trained on more than 1,500 manually annotated event mentions.