By harnessing aspects of quantum mechanics, communication and information processing could be radically transformed. Promising forms of quantum information technology include optical quantum cryptographic systems and computing using photons for quantum logic operations. As with current information processing systems, some form of memory will be required. Quantum repeaters, which are required for long distance quantum key distribution, require quantum optical memory as do deterministic logic gates for optical quantum computing. Here, we present results from a coherent optical memory based on warm rubidium vapour and show 87% efficient recall of light pulses, the highest efficiency measured to date for any coherent optical memory suitable for quantum information applications. We also show storage and recall of up to 20 pulses from our system. These results show that simple warm atomic vapour systems have clear potential as a platform for quantum memory.