I got my nephew and niece phones when they were 8 and 10, respectively. They are on my family plan. I have bought them each three phones over the years, increasing the abilities of the phones as the kids matured. My niece is now 12, and my nephew is about to turn 14. I plan on getting them iPhones for Christmas. They have been very responsible. I think it depends on the particular child, though. Some kids are more responsible than others.
For my niece and nephew, it makes sense. They have spent hours getting to know my iPhone, and they really appreciate all it can do. Kids are very tech savvy these days, and they want more than "just a phone." I can't wait for Christmas to give them theirs! Plus, since they can't buy stuff over the iPhone other than on the WiFi iTunes music store (they would have to pay, not me), and since there are no ridiculous subscription services available, I feel safer financially (no possible surprise charges on the bill, although they have never done that to me before). The iPhone data plan is actually cheaper than the MediaNet plan I have them on now, so my bill will go down while giving them more Internet than they get now, as well. It's a win-win situation!
I have told them that this is the last time I am buying them phones (yeah, right, I can't really be sure of that - I do spoil them - but they think this is the last time), and that if they lose them or break them, they will have to replace them on their own. They know how expensive they are, and they have agreed. But like I said, it depends on the kid. If my niece and nephew were irresponsible or clueless about the value of things (especially money), then I wouldn't do it.