I think that a child's personality plays a huge role in determining a good starting age for camp. When we first considered sending our eldest to camp for a week, we thought about how he had handled major new situations in the past. These included the first day of school, the first sleepovers at a friend's house, how he handled his first week of day camp, how he did when taking swimming lessons for the first time, etc. And we also thought about how well he adapts to minor changes as well. For kids who had trouble with situations like these when younger, how do they adapt now?
My eleven-year-old started going to camp last summer, and has loved it both years. I went to camp starting at age 9 and continued through 15. I felt a bit homesick sometimes when I was younger, but the activities that I got to do were the kinds of things that I never would have been able to do daily or weekly at home: sailing, waterskiing, horseback riding, archery, canoeing and capsizing, Christmas in July, etc. I still look back on it as one of the most wonderful experiences of my youth.
Obviously, it's not for everyone, though (see paragraph 1).