Nice op-ed in The Times suggesting that while brain exercises don't actually do much for your brain, actual exercise has been proven to do quite a bit.
When inactive people get more exercise, even starting in their 70s, their executive function improves, as shown in a recent meta-analysis of 18 studies. One effective training program involves just 30 to 60 minutes of fast walking several times a week.
Exercise is also strongly associated with a reduced risk of dementia late in life. People who exercise regularly in middle age are one-third as likely to get Alzheimer's disease in their 70s as those who did not exercise. Even people who begin exercising in their 60s have their risk reduced by half.
Widespread distribution of those benefits would vastly reduce dementia (not to mention cardiovascular disease, obesity, etc), thus lowering health costs. But, instead, we've pumped enormous amounts of money and constructed our building codes such that walking, in many communities and areas, is basically impossible, particularly for the elderly, who are less adept at dodging cars.