Greg Bernhardt said:
I love scrabble, I would think that is also a good mind game.
As with crossword puzzles, there are a number of studies which show benefits in overall cognition (not overall, but day to day intelligence basically) from Scrabble, and similar games. Any game that makes you associate immidiate stimuli with thoughtful recall of memory, and then synthesis to make it work, seems to confer a similar benefit.
The study I mentioned about video games showed that even "non-gamers" improved ~15% on the tests given after a series of brief gaming sessions. "Gamers" seemed to score ~33% (this is from semi-dim memory, hence the prox) on those same tests. Now, one might argue those tests don't actually measure a real improvement, but it seems to be a logical extension of gaming overall.
There is also one other element: FUN.

Who knows how much of this is just the result of us being deeply engaged in a mentally taxing AND fun activity? We're animals with a long history of needing to play games, to learn, and to reinforce lessons. I'm not surprised that play needs to be a constant part of our lives.
EDIT: Here are a couple of studies/letters/articles which are not hyping anything, but exploring aspects of HOW games modify attention, improve some elements of cognition, etc:
Also, the recent study checked IQ, and other Intelligence tests... and I don't think reasonable people believe that overall intelligence as measured is likely to improve OR decline in the absence of disease or some radical new drug. Improving memory, vocuabulary, recall... these were not measured.
http://www.bcs.rochester.edu/people/Daphne/GreenandBavelier.pdf
http://www.springerlink.com/content/j7526154022g3532/