Implementing on-chip non-volatile photonic memories has been a long-term, yet elusive goal. Photonic data storage would dramatically improve performance in existing computing architectures by reducing the latencies associated with electrical memories and potentially eliminating optoelectronic conversions. Furthermore, multi-level photonic memories with random access would allow for leveraging even greater computational capability. However, photonic memories have thus far been volatile. Here, we demonstrate a robust, non-volatile, all-photonic memory based on phase-change materials. By using optical near-field effects, we realize bit storage of up to eight levels in a single device that readily switches between intermediate states. Our on-chip memory cells feature single-shot readout and switching energies as low as 13.4 pJ at speeds approaching 1 GHz. We show that individual memory elements can be addressed using a wavelength multiplexing scheme. Our multi-level, multi-bit devices provide a pathway towards eliminating the von Neumann bottleneck and portend a new paradigm in all-photonic memory and non-conventional computing.