What is the effect of aging on chess ability? Based on documented evidence, at what age would someone normally expect to see his chess results start to decline?
According to this study chess grandmasters peak at age 31.4. 

This study confuses the hell out of me, but there is one sensible chart at page 20, that seems to indicate that you can still improve a little bit in your thirties and generally hold your playing level into your mid-forties. After that the decline becomes noticable. 

The slight discrepancy between these two studies is easily explained by the fact that the first only looks at grandmasters, whereas the second examines more than 40,000 players. In fact I would assume that the very top players peak even earlier these days. 

I found a very good chess.com article about this topic. This guy analysed more than 71,000 players and found a rating peak in the late twenties. Until you are eighty you'll lose 200 Elo points on average, which really isn't all that much.