HPC today faces new challenges due to paradigm shifts in both hardware and software. The ubiquity of multi-cores, many-cores, and GPGPUs is forcing traditional serial as well as distributed-memory parallel applications to be parallelized for these architectures. Emerging applications in areas such as informatics are placing unique requirements on parallel programming tools that have not yet been addressed. Although, of all the available parallel programming models, task parallelism appears to be the most promising in meeting these new challenges, current solutions for task parallelism are inadequate. In this paper, we introduce PFunc, a new library for task parallelism that extends the feature set of current solutions for task parallelism with custom task scheduling, task priorities, task affinities, multiple completion notifications and task groups. These features enable PFunc to naturally and efficiently parallelize a wide variety of modern HPC applications and to support the SPMD model of parallel programming. We present three case studies: demand-driven DAG execution, frequent pattern mining and iterative sparse solvers to demonstrate the utility of PFunc's new features.