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I recently googled relevant psychology, neuroscience, aging, and education websites to get a sense of the kind of research being conducted on the relation between puzzles, and general brain functioning. I found an astronomical number of sites. I then looked up sources that I considered to be scientifically reliable ones. Much of the research in this domain turns out to be ambiguous, and certainly not as optimistic as it is claimed to be by the media. For example, a study published in Brain and Cognition (Volume 46, 2001, pp. 95-179) showed that the elderly performed significantly poorer on the Towers of Hanoi puzzle than younger subjects. The puzzle-in case you are not familiar with it-consists of three pegs requiring solvers to move the concentric disks placed on the left peg in order from the smallest on top to the largest on the bottom to the right peg so that at no point in the movement of the disks can a larger one rest on top of a smaller one. Direction of movement is not restricted.
Another study examining crosswords and aging published in the Journal of Experimental Psychology (Volume 128 . 1999, pp. 131-164) found no evidence to suggest that crossword puzzle experience reduces age-related decline in cognition. However, in other work, one of the researchers, E. J. Meinze, found evidence to suggest that a high level of experience with crosswords in older subjects does seem to partially attenuate the negative effects of age on memory and perceptual speed tasks (Psychology of Aging, Volume 15 , 2000, pp. 297-312).