We present an auto-tuning system for optimizing I/O performance of HDF5 applications and demonstrate its value across platforms, applications, and at scale. The system uses a genetic algorithm to search a large space of tunable parameters and to identify effective settings at all layers of the parallel I/O stack. The parameter settings are applied transparently by the auto-tuning system via dynamically intercepted HDF5 calls. To validate our auto-tuning system, we applied it to three I/O benchmarks (VPIC, VORPAL, and GCRM) that replicate the I/O activity of their respective applications. We tested the system with different weak-scaling configurations (128, 2048, and 4096 CPU cores) that generate 30 GB to 1 TB of data, and executed these configurations on diverse HPC platforms (Cray XE6, IBM BG/P, and Dell Cluster). In all cases, the auto-tuning framework identified tunable parameters that substantially improved write performance over default system settings. We consistently demonstrate I/O write speedups between 2x and 100x for test configurations.