Just to add to Jens answer, opinion is still divided regarding whether memory is subserved by distinct systems, or is a distributed, emergent property of perceptual, navigational and semantic systems. Whereas patient data has always strongly implicated distinct memory systems (e.g., declarative vs non-declarative), multivariate fMRI studies have provided good support for reinstatement theories, where successful retrieval of memories involves reinstatement of perceptual states. Moreover, there is growing evidence that regions that are thought to be amodal memory structures (e.g., hippocampus, perirhinal cortex), are involved in perceptual discrimination judgements and show preferences for different categories of visual input. For example, damage to the hippocampus can impair scene discrimination judgements whereas damage to the perirhinal cortex can impair face and object discrimination judgements. So it could be the case that there really aren't any dedicated memory structures per se, but memory is the co-ordinated reactivation of mechanisms involved in perception and action (probably via top down signals from frontal lobes).
The references provided by Jens provide good coverage of the distinct systems view of memory so I'll just provide some references for the distributed and reinstatement views.
Murray, E. A., Bussey, T. J., & Saksida, L. M. (2007). Visual perception and memory: A new view of medial temporal lobe function in primates and rodents. Annual Review of Neuroscience, 30, 99-122.
Graham, K.S., Barense, M.D. & Lee, A.C.H. (2010). Going beyond LTM in the MTL: a synthesis of neuropsychological and neuroimaging findings on the role of the medial temporal lobe in memory and perception. Neuropsychologia, 48, 831-853.
Polyn S.M., Natu V.S., Cohen J.D., & Norman K.A. (2005) Category-specific cortical activity precedes recall during memory search. Science, 310, 1963-1966.
Johnson, J. D., McDuff, S. G. R., Rugg, M. D., & Norman, K. A. (2009). Recollection, familiarity, and cortical reinstatement: A multivoxel pattern analysis. Neuron, 63, 697-708
Xue G, Dong Q, Chen C, Lu ZL, Mumford JA, Poldrack R (2010). Greater Neural Pattern Similarity Across Repetitions is Associated with Better Memory. Science, 330, 97-101.