I think it depends on the child and not really the age, I have an older brother so his consoles were my introduction to gaming, I was playing the Master System from age 4 then the Mega Drive at age 6, and had my own personal GameBoy at 8, which I took really good care of.
If the child is old enough to be able to understand and play the game then go for it I say, everyone has childhood memories of favourite toys, movies and tv shows that they still hold dear, me to, but mine are also full of great memories of games that I loved.
Just be on guard of age rating on games, it's usually there for the content of the game but it's also there because some games are just to advanced for certain age groups, no point wasting your money on a game that's never gonna get played.