Absolutely. In fact, identity thieves place a high premium on stolen Social Security numbers of minors, because it can often be a very long time before the theft is discovered: imagine going to apply for a credit card for the first time, only to find out that someone else had been using your identity for years! If you're considering an identity theft protection plan, be sure to find out what options are available for the children in your family: their coverage is usually deeply discounted when compared with the costs for adults.