Fyi, speaking of Lumosity, research on training working memory with the hope of transferring those gains to other intelligence measures is inconsistent and equivocal. Of course, I still play those kinds of games because they're short, fun, and addicting :)
Most individual gains are likely due to repetition and practice, BUT those gains might only be tailored to that specific game's task (i.e., doing better at the game is less likely to transfer over to improved fluid intelligence, and game performance may not measure what researchers think they're measuring).
Significant limitations of some previous studies include lack of actively engaged control groups (as opposed to passive or "no contact" ones); inappropriate collation of task performance data from heterogeneous groups and tests; generous extrapolation from results of one-dimensional metrics claiming to represent more complex cognitive abilities; and publication bias suffering from the "file drawer problem" (the proportion of unpublished negative results are likely high).
This study from 2013 includes a nice review: http://www.researchgate.net/publication/227340699_No_Evidence_of_Intelligence_Improvement_After_Working_Memory_Training_A_Randomized_Placebo-Controlled_Study
They found that despite significant improvements on working memory training tasks, the subjects demonstrated no positive transfer to fluid intelligence, multitasking, working memory capacity, crystallized intelligence, or perceptual speed tasks. Interestingly, individuals subjectively reported feeling an increase in their cognitive abilities afterwards despite no improvement by any objective performance measure!
More variables need to be teased apart, though, so some potential benefit in certain populations for aspects other than working memory isn't quite settled yet.
(Some studies in special populations of adult stroke patients, epileptics, children treated for brain cancer, etc. indicate some weak correlation between game practice and selective cognitive improvement, but mostly not more than those seen in controls, however.)Edit:
Another great discussion of a study in Nature from 2010: http://blog.brainfacts.org/2013/05/how-can-we-enhance-working-memory/#.VkeNEnarS00