We present a platform independent runtime interface for moving data and computation through parallel machines with multi-level memory hierarchies. We show that this interface can be used as a compiler target and can be implemented easily and efficiently on a variety of platforms. The interface design allows us to compose multiple runtimes, achieving portability across machines with multiple memory levels. We demonstrate portability of programs across machines with two memory levels with runtime implementations for multi-core/SMP machines, the STI Cell Broadband Engine, a distributed memory cluster, and disk systems. We also demonstrate portability across machines with multiple memory levels by composing runtimes and running on a cluster of SMP nodes, out-of-core algorithms on a Sony Playstation 3 pulling data from disk, and a cluster of Sony Playstation 3's. With this uniform interface, we achieve good performance for our applications and maximize bandwidth and computational resources on these system configurations.