[Off-topic] Pennycake:
"Teenager" covers a large range - a 13 year old is much different from someone who is 19 and perhaps away from home at college. I'm going to narrow this down to 13-18.

Things might change in the future, but currently, I don't think a smartphone is necessary during high-school. If the school supported it, I think a netbook would be a better investment.

If the kid wants a smartphone and it's more than a usual gift, I'd say let them save up and buy it. That teaches responsibility - being able to save money and being able to find work (be it working on Saturdays at a local store or doing things for neighbours), and they'll know the value of the object they've bought when they've had to save up weeks or even a whole summer for it - you're not going to let that thing out of your sight if it took you a couple months to earn with your own labour (and if you do, you've got a grade-A case of carelessness that nothing's going to fix, except perhaps repeated months of working to replace what you broke).

Managing money is something a lot of parents do not adequately teach their children - and this has been found to be true across most income levels. It is an important skill to learn, from which parents often shelter children. There's something to be said for blissful, ignorant happiness that comes with not knowing about bills and how long you, the parent, had to work to pay them. But once children are reaching the age when they can reasonably be expected to care for a $600 phone, they're old enough to start learning about financial issues.

While my smartphone has been helpful, most of the important things that have made major improvements in my life are things I did on my "dumb-phone", so I can't say I feel that a high-school student is going to benefit all that much from having one. My biggest benefits are not school related - although relevant to college life when you consider ability to navigate on the fly - not having to ask a potentially shady place or person for directions, not being lost and wandering somewhere inhospitable, et cetera.

Having Astrid (to-do list app) really changed my life, and I do wonder how much it would have helped in high-school. I have a relatively mild case of ADD and having a to-do list, able to sync across platforms and remind me of things, helps me enough that it justifies the cost of the phone on its own. I could see that if I had a child who was struggling with something similar, that it would be beneficial to have a talk about it and consider something age-appropriate (ie, budget smartphone with extra-rugged case).

I learned the most about life and how to get things done when my parents stopped trying to micro-manage my life. It's important to want to hold yourself accountable. I have learned so much and have helped friends who were less-prepared by their parents. For instance, I'm extremely lucky my first job when I was 18 gave me a credit card - I now have a pretty good credit score (>720) while many other people my age are plagued by "insufficient credit history" and unable to complete simple financial transactions without a parent to co-sign (and in less well-off families this is sometimes not an option - which makes starting your own good history even more important). Many don't know how to do the most basic things - everything from being able to find good deals to filing their taxes.

Paying for a pre-paid plan after saving up for a smartphone is a great way to introduce them to many important "adult" concepts - everything from doing good product research (a skill that will serve them well for everything from buying their first car to first house), to saving money, to the value of work, to the importance of making payments on time - and more.