The increasing availability of structured data in Resource Description Framework (RDF) format poses new challenges and opportunities for data mining. Existing approaches to mining RDF have focused on one specific data representation, one specific machine learning algorithm or one specific task, only. Kernels, however, promise a more flexible approach by providing a powerful framework for decoupling the data representation from the learning task. This paper focuses on how the well established family of kernel-based machine learning algorithms can be readily applied to instances represented as RDF graphs. We first review the problems that arise when conventional graph kernels are used for RDF graphs. We then introduce two versatile families of RDF graph kernels based on intersection graphs and intersection trees. These kernels can better exploit the inherent properties of RDF, while providing an easy to use interface between any RDF graph (including vocabulary extensions such as RDFS and OWL) and any kernel-based learning algorithm (which are available for solving many machine learning tasks). The flexibility of the approach is demonstrated on two common relational learning tasks: entity classification and link prediction. The results show that our novel RDF graph kernels with standard SVMs achieve competitive predictive performance when compared to specialized techniques for both tasks.