We introduce the Balsam service to manage high-throughput task scheduling and execution on supercomputing systems. Balsam allows users to populate a task database with a variety of tasks ranging from simple independent tasks to dynamic multi-task workflows. With abstractions for the local resource scheduler and MPI environment, Balsam dynamically packages tasks into ensemble jobs and manages their scheduling lifecycle. The ensembles execute in a pilot "launcher" which (i) ensures concurrent, load-balanced execution of arbitrary serial and parallel programs with heterogeneous processor requirements, (ii) requires no modification of user applications, (iii) is tolerant of task-level faults and provides several options for error recovery, (iv) stores provenance data (e.g task history, error logs) in the database, (v) supports dynamic workflows, in which tasks are created or killed at runtime. Here, we present the design and Python implementation of the Balsam service and launcher. The efficacy of this system is illustrated using two case studies: hyperparameter optimization of deep neural networks, and high-throughput single-point quantum chemistry calculations. We find that the unique combination of flexible job-packing and automated scheduling with dynamic (pilot-managed) execution facilitates excellent resource utilization. The scripting overheads typically needed to manage resources and launch workflows on supercomputers are substantially reduced, accelerating workflow development and execution.