The Resource Description Framework (RDF) and SPARQL query language are gaining wide popularity and acceptance. In this paper, we present DREAM, a distributed and adaptive RDF system. As opposed to existing RDF systems, DREAM avoids partitioning RDF datasets and partitions only SPARQL queries. By not partitioning datasets, DREAM offers a general paradigm for different types of pattern matching queries, and entirely averts intermediate data shuffling (only auxiliary data are shuffled). Besides, by partitioning queries, DREAM presents an adaptive scheme, which automatically runs queries on various numbers of machines depending on their complexities. Hence, in essence DREAM combines the advantages of the state-of-the-art centralized and distributed RDF systems, whereby data communication is avoided and cluster resources are aggregated. Likewise, it precludes their disadvantages, wherein system resources are limited and communication overhead is typically hindering. DREAM achieves all its goals via employing a novel graph-based, rule-oriented query planner and a new cost model. We implemented DREAM and conducted comprehensive experiments on a private cluster and on the Amazon EC2 platform. Results show that DREAM can significantly outperform three related popular RDF systems.