I grew up playing fantasy roll playing games. This answer is quite long, but I am trying to give a full description of the game.
As long as he is able to separat fantasy from reality, and it is done with parental supervision for a while, it can be a great way to express creativity and problem solve and tell stories. And it's a fun way of applying math, which can often catch a kids attention and help him feel confident in math more than any tutoring program (my brother's math became stronger - even though at first he was counting dots on the dice.)
D&D can be a bit complicated at first. You'll want to make sure that YOU understand the rules and how the whole thing works, so you can help him with it. I would go with the most recent version (there have been several, some more complicated than others). Also, keep in mind that this game is meant to be interactive. It works ok with 2 players, but is much better with more; generally one player is the "Dungeon Master" (aka DM), and that person creates the scenario for the other players. The other players create characters, and then play out the scenarios. This can take anywhere from an hour or two to several hours or more (sometimes with 'to be continued') Think of it as a structured game of make-believe. And they use dice to determine "did you succeed" or "how much damage did you do" so there is less bickering about that :)
Again, I would strongly suggest parental supervision for the first few years. Better yet, get involved and play yourself. This is the best way to help him understand what is and is not acceptable play (to fit your family's values etc). You can also help him understand the whole problem solving thing more. And its great tim spent together.
If he really gets into it, as he gets older (teens) he may find other kids who play similar games. Many kids (and adults) will set up "game nights" where they get together and spend hours playing. You will have to decide how often and how long these can be (but it is still better than hours in front of a video game). We generally gamed about once a month, on a saturday evening. Also, know the kids and their parents - know the environment he's going to just like any other situation. You may be more comfortable hosting these games yourself. And be aware of the financial - he may want figures and environment, and photocopies for the character sheets, and such.
Back in the 1980's there was a big scare that D&D was a horrible, satanic, cult-based game. I think this came from a small amount of kids who used it a vehicle for such (expressing their own decisions through the game and then using it as a scapegoat). Fantasy roll playing is a great way to foster creativity, story telling, problem solving, cooperation, negotiation, etc. Just make sure you know and understand what your child is doing (no matter what game or activity he is into).