Ontologies and rules play a central role in the development of the Semantic Web. Recent research in this context focuses especially on highly scalable formalisms for the Web of Data, which may highly benefit from exploiting database technologies. In this paper, as a first step towards closing the gap between the Semantic Web and databases, we introduce a family of expressive extensions of Datalog, called Datalog±, as a new paradigm for query answering over ontologies. The Datalog± family admits existentially quantified variables in rule heads, and has suitable restrictions to ensure highly efficient ontology querying. We show in particular that Datalog± encompasses and generalizes the tractable description logic EL and the DL-Lite family of tractable description logics, which are the most common tractable ontology languages in the context of the Semantic Web and databases. We also show how stratified negation can be added to Datalog± while keeping ontology querying tractable. Furthermore, the Datalog± family is of interest in its own right, and can, moreover, be used in various contexts such as data integration and data exchange. It paves the way for applying results from databases to the context of the Semantic Web.