Hardware enclaves such as Intel SGX are a promising technology for improving the security of databases outsourced to the cloud. These enclaves provide an execution environment isolated from the hypervisor/OS, and encrypt data in RAM. However, for applications that use large amounts of memory, including most databases, enclaves do not protect against access pattern leaks, which let attackers gain a large amount of information about the data. Moreover,the naive way to address this issue, using Oblivious RAM (ORAM) primitives from the security literature, adds substantial overhead. A number of recent works explore trusted hardware enclaves as a path toward secure, access-pattern oblivious outsourcing of data storage and analysis. While these works efficiently solve specific subproblems (e.g. building secure indexes or running analytics queries that always scan entire tables), no prior work has supported oblivious query processing for general query workloads on a DBMS engine with multiple access methods. Moreover, applying these techniques individually does not guarantee that an end-to-end workload, such as a complex SQL query over multiple tables, will be oblivious. In this paper, we introduce ObliDB, an oblivious database engine design that is the first system to provide obliviousness for general database read workloads over multiple access methods. ObliDB supports a broad range of queries, including aggregation, joins, insertions, deletions and point queries. We implement ObliDB and show that, on analytics work-loads, ObliDB ranges from 1.1-19x faster than Opaque,a previous oblivious, enclave-based system designed only for analytics, and comes within 2.6x of Spark SQL. ObliDB supports point queries with 3-10ms latency, which runs over 7x faster than HIRB, a previous encryption-based oblivious index system.