The exception is a lap child - a BC can be required to prove the child is under 2 and eligible to fly for free on a parents lap.
TJ
My son was 17 when we flew down last August and, like a PP said, looked older, so he was asked. When he said he was 17, the person at security informed us it didn't matter how old he was he had to have a photo ID.
Luckily, I had brought along his previous years school ID (we hadn't even started for the year here, he didn't have a current one) and his ID and she very grudgingly accepted that as ID.
I would say, only as caution, that you should bring a school ID if your child is old enough to have one. My son is a big guy and I suspect she thought he was well over 18 because he could look it, so little mom next to him saying he was only 17 probably didn't seem right.
Ress
I'm Canadian so my situation is a bit different, but the one thing I have discovered is that I use my passport all the time. I always grab it when I fly whether domestically or (or course) into the US. It's the one form of ID that is always acceptable and never questioned. We have passports for the kids, too and use them regularly, not just for travel. It's nice to know that we'll be prepared if we're ever diverted to a US airport because of weather or other cause, too.
On another note it is a great idea to have a copy of your child's social security card and birth certificate available. Several years ago, I had to take my child to a "medical center" kind of like a walk in hospital. Luckily, I always have my BlackBerry and I had e-mailed myself those documents sometime in the past. I was able to forward the documents via e-mail to the nurse. They told me that they would not have treated her without either payment in full or an insurance card plus identification.
You can put this data on a camera's SD card or a jump drive to be certain that you always have it with you. I also e-mail myself copies of the tickets to Disney and to the MNSSHP just in case they got lost.
Unfortunately the TSA agent was wrong - and if a TSA agent is going to require an ID then a school ID isn't an acceptable form if ID.
Many 16 and 17yo's do have a drivers license and if so should be prepared to show it. If your teen looks as if he/she could be 18 then I would probably bring a passport or get a walking ID from the DMV as both are listed as acceptable forms of ID.
Otherwise IMHO there is no need to scramble around and find ID's for children under 18 (other than a BC for a lap child).
Here is the info right from the TSA:
"Effective June 21, 2008, adult passengers (18 and over) are required to show a U.S. federal or state-issued photo ID that contains the following: name, date of birth, gender, expiration date and a tamper-resistant feature in order to be allowed to go through the checkpoint and onto their flight. "
http://www.tsa.gov/travelers/airtravel/acceptable_documents.shtm
I fly several times a year with my kids and they have never, ever been asked for ID.
TJ
Just for peace of mind I always travel with copies of my kid's birth certificates. I just think it's a simple thing to do and you never know when you might need it. I keep it in the folder of important papers and throw it in the hotel room safe when we arrive.
The only time I've been asked for it was on our trip with DD as a lap baby, she was 18 months old and has always been tall so I had to prove she was under 2. No problem, just whipped out the copy of her b.c. and everything was good.
Peace of mind is one thing.
What is required is another.
Children under 18 do not need any kind of ID to travel domestically unless they are traveling on some kind of age-restricted fare of, as the PP noted, as a lap baby without a ticket.