Today's high-performance computing (HPC) systems are heavily instrumented, generating logs containing information about abnormal events, such as critical conditions, faults, errors and failures, system resource utilization, and about the resource usage of user applications. These logs, once fully analyzed and correlated, can produce detailed information about the system health, root causes of failures, and analyze an application's interactions with the system, providing valuable insights to domain scientists and system administrators. However, processing HPC logs requires a deep understanding of hardware and software components at multiple layers of the system stack. Moreover, most log data is unstructured and voluminous, making it more difficult for system users and administrators to manually inspect the data. With rapid increases in the scale and complexity of HPC systems, log data processing is becoming a big data challenge. This paper introduces a HPC log data analytics framework that is based on a distributed NoSQL database technology, which provides scalability and high availability, and the Apache Spark framework for rapid in-memory processing of the log data. The analytics framework enables the extraction of a range of information about the system so that system administrators and end users alike can obtain necessary insights for their specific needs. We describe our experience with using this framework to glean insights from the log data about system behavior from the Titan supercomputer at the Oak Ridge National Laboratory.