We present PLSQLBench, to our knowledge the first benchmark for evaluating whether LLMs can write executable PL/SQL programs, with correctness measured through execution-based tests. Existing LLM evaluations largely target general-purpose code generation or declarative text-to-SQL, leaving procedural database programming underexplored. PLSQLBench contains 2,865 instances: 2,594 single-turn tasks and 271 multi-turn conversations spanning 978 turns. The benchmark combines complex schema-grounded tasks over enterprise-style Spider 2 databases, simpler schema-grounded tasks derived from Spider, and MBPP-derived procedural problems, covering varying levels of database grounding and procedural complexity. Experiments with eight LLMs reveal recurring difficulties in schema grounding, PL/SQL dialect fidelity, procedural control flow, exception handling, and cross-turn consistency. Tool-augmented LLM agents improve performance on several schema-grounded evaluations, although substantial gaps remain. These results highlight procedural database-programming capabilities not directly assessed by conventional code-generation or text-to-SQL benchmarks. Our code is available at https://github.com/oracle-samples/plsqlbench.