Since roleplaying games deal so much with the mind and imagination, it can be difficult to measure their benefits. With physical sports the results are easy to see, even with the naked eye: weight loss, increased coordination, and so on. But roleplaying games exercise thinking, reacting, verbal and mathematical skills, and teamwork that can be accomplished while everyone remains sitting. So when we discuss the benefits of roleplaying games, we discuss what has been observed but not statistically measured. That should not diminish the value that roleplaying games have had in a great many lives.
The first benefit that comes to mind involves reading. Roleplayers end up reading a great deal simply to learn more about the games they want to play; for those parents who have difficulties getting their children to read, roleplaying games can be a help. Some roleplaying systems use obscure terminology that nonetheless can be useful to know (it is from White Wolf games that I readily remember such terms as obfuscate, vicissitude, and umbra). Roleplayers also get to exercise their verbal skills, since roleplaying games are heavily dependent on description.
On top of all of this, gamers often like to research particular eras of history in order to learn more about historical game settings. In high school, I ended up doing research just for my hobby and I learned things outside of class. Roleplaying games also tend to involve various levels of mathematics. Roleplayers are often called upon to quickly perform various math functions to decide the outcome of different actions in the game. Unless a system is based entirely on description, math will be required somewhere.
It is also important to remember that roleplaying games are, by their very nature, social activities. Although they are not team sports like football, requiring a particular line-up of members, roleplaying games need at least two people and often encourage the formation of groups for more interactivity. This not only helps form friendships but it also gives kids a way to socialize outside of school. If parents are willing to host games at home, they can feel good knowing exactly where their children are and precisely who they're with.
Instead of doing drugs, engaging in risky sexual behaviors, or acting out against the law, a good many teenagers spend their weekend nights safely in a house, rolling dice and perhaps drinking too much caffeine. This is not to say that roleplaying games can't be misused, like any other sort of social event. Some people bring negative influences into their games to various degrees but gaming books do not encourage this behavior. Most gamers end up like most baseball fans: gathering together for a night of entertainment.