I can think of many phones that won't require data. Read my comment to Backnblack.I think thats a little short sighted. Many phones that arent smart phones are now requiring a $10/mo data plan on top of the $10 add a line.
It has nothing to do with wanting a data plan on a phone and/or making the kid pay for it. I have a 10yr old that has no desire for a data plan. On the pre-paid phone he has now he has access to data but does not use it. We were considering getting him a phone through VZW so its all free txt + mobile to mobile but now many phones that he would like also will require a $10/mo data plan EVEN IF HE DOESNT USE IT.
There are PLENTY of phones that will get you free text via mobile to mobile and will share your family's minutes that won't run you any monthly cost in data. They're called dumbphones, and VZW has plenty of them. Do you want me to link you all of them from VZW's website? There's a lot of them.
The problem here isn't that there aren't phones for your desired purpose, but that your kid thinks the phone is ugly or is trying to talk you into getting him/her a phone that does more than talk & text. Well, be a parent and grow up and learn to tell your kid no, this is all you get, so learn to deal with it.
When I was a kid, and it wasn't all that long ago, I had a cell phone at 16 that my parents paid for. I didn't like it, it was a brick and it was ugly and it had T9 texting, but I used it to text & call and that was it. It never did anything else, but I learned to live with it because it was all my parents would pay for. Life went on, certainly.
If your kid doesn't want one of those phones because they are ugly or something, tell him/her to get over it. If they want to pay the bill, fine, they can get whatever they want. Be a parent and stand up for yourself and make the rules. Tell your kid it doesn't matter if a phone is ugly or not, that isn't the point; the point is that they have a mobile phone that can place calls and compose text messages for necessary things like texting "hey dad, done in 5 min, come get me from bball practice".
Cell phones aren't toys. Err, the iPhone is, but it isn't a very good phone so think whatever you want. Regardless, if your kid wants a phone that plays games and browses the web, they probably don't need to browse the web, and you can buy them a Nintendo DS or PSP that will play games on the go, and paying for AA batteries is a lot cheaper than paying $10-$30 per month for a data plan.