Over this last Christmas I introduced my then 7 year-old nephew to D&D via the new Basic Set. He loved it. In fact, in a strange moment in my life as a gamer, my parents for the first time ever showed an interest in the game. It was an interesting scene, my nephew, two of my sisters, my nephew's step-father, a boyfriend of one of my sisters, my wife and I sat around the table playing, while my other sister (the nephew's mother), her daughters, and my parents sat around the periphery watching us play, getting as excited by the events as we were.
The next month I sent my nephew the Basic set for his eighth birthday along with Matt Forbeck's D&D book for young readers.
To put this all in the context of kids and their varying maturity and intellegences: My nephew is quite good with math, but was struggling with reading (in fact at the bottom of his class). He has since his birthday read the book I sent and the rules of the Basic set. He has made a concerted effort to work on reading because he is now excited to use that skill. He has begun writing his own adventures for friends and creating new characters. One of the signs to me that he really "got it" was that after that first night, when he insisted on naming his character Gandalf, he bagan creating his own names for characters that were reminiscent of other characters he likes (his Sorcerer is now named Kendabi, after Obi-Wan).
I live in New York, and my nephew lives in Minnesota. I usually only see him about twice a year (at Christmas and again in the summer). My wife and I are going to MN in August for one of my sisters' wedding, and my nephew and I have been talking on the phone regularly about playing D&D again.
I had been very worried that the Basic set might even be too much for him at first. But he rose to the occasion. I think if the child is shown how fun it is before introducing all the rules and record-keeping, it inspires him/her to make an effort to learn how to play.
I guess this sounds a bit too much like an ad for the Basic game and how it "changed a life". But it was really a great experience, and I highly recommend introducing your nephew to the game. Even if you only get to play twice a year, it is something fun you can talk about on the phone and in letters (I occasionally send a letter with images from the D&D online art gallery printed on the page).
In a couple of years my nieces will be getting old enough to play, and I can't wait to bring them into the fold as well.