I remember a speech by Adele Goldberg on a conference about History Of Programming Language; it was about successful experiments to teach Smalltalk to pre-highschool children. You can find about this here: http://gagne.homedns.org/~tgagne/contrib/EarlyHistoryST.html#smalltalkAndChildren.

Most responses to your question say: As soon as there is interest. This is certainly (I would almost say: trivially) true, but it applies to the rare cases where a certain bright child starts showing interest, and you are teaching him or her individually. The question of age becomes more serious when you want to offer a teaching for a class of students, i.e., at which age can you expect that a sufficient percentage of children is able to grasp abstractions - assuming here that the necessity of doing some abstract thinking is the biggest stumbling point, even for adults. I still remember when, at the age of 16, our class was the first time exposed to programming. It was an optional subject, and nearly the whole class showed interest and attened. But after a few months, only about 10% were left - it was too difficult for the rest. Nowadays teaching has improved, so I guess the percentage would be much higher now, though.

IMO it makes sense looking where we request abstract thinking in other areas. This can be mathematics, as soon as it leaves pure calculation and introduces concepts such as functions or group theory, and languages as soon as it starts to cover grammatical concepts. For the average student, I guess this means they should be at least 10-12 years, though some very gifted ones might be able to master it earlier.