My son got one for his 7th birthday, and a few of his friends got them for their 8th birthdays (he's on the young side). It's very appropriate for him. I have told my almost 5 year old that she has to learn to read before I'll buy her one. She has a leapster, and even if she's reading fluently tomorrow, she'll still have to wait for a DS.
For anyone who thinks their child might be too young, consider our recent experience. This morning DS could not find his game. He had it last night in the car, fell asleep with it on his lap, woke up & went inside without it, as far as anyone could remember. He searched the car several times, as did I. We didn't know if it had fallen out of the car or been stolen or what. The thought of replacing it and the games in it at the time (Animal Crossing $35 and Pokemon Emerald for GBA $17 used) plus the system for $129 made us all sick. DS cried, hit his sister for taking it, threw things. It was ugly.
Finally, DH searched the car yet again, quadruple checking under the front seat, and there it was. Maybe this was DS's fault, maybe it wasn't, but he got a talking to about his attitude and lack of responsibility for his things in general. It's not the first time he's misplaced it.
It's made me re-think getting him a cell phone when we change to a new plan. I want him to have one for emergencies but not if it's going to get lost, broken or stolen.