It's not exactly a new thing, but the Washington Post reported on the latest episode of a child spending hundreds -- actually $1,400 -- on in-app purchases. In this case, the 8-year-old was buying Smurfberries to decorate the Smurfs' Village app. You can spend up to $99.99 for a single in-app purchase of the berries. Apple provided the family a refund after the mother received the bill.
The article points out that these sorts of purchases are being blamed on Apple since there is a 15-minute window (after authorizing a previous App Store buy) where a password is not needed to make another purchase. Yes, Apple should add the option to require a password no matter how much time has passed or have parental controls be the default setting on an app, but a child could still potentially figure out a password and toggle the option off.
In the end, it is up to the parents to make sure that the child's access to in-app purchases on any device is restricted. Do not give your password to your child, or link your App Store account to a credit card with a very small credit line that cuts off when it reaches its limit.
Apple is not the only company out there to have in-app or in-line purchases. You can get Facebook credits for its games just as easily -- however, since Facebook's terms of service forbid young children from using the social network, presumably the Farmville players have a bit more adult judgement to help them avoid unexpected costs.