I've been watching this show since season two, which was airing when I was 11-12. Honestly, Supernatural changed me for the better.
The mythology of the show inspired me to learn more about other cultures and religions. Each episode brings something new to the table - a new creature, lore from all over the world, so much information about different cultures. This show, I think, is what really got me into history and culture from a young age.
That's not all that's good about Supernatural. While the show looks like two guys shooting monsters to an outsider, any fan can tell you that that's not really what it's about. Supernatural, at its very core, is a tale of two brothers who would die for each other (and do, several times over). This show is all about loyalty to friends and family, and the importance of loving one another. Sam (Jared Padalecki) and Dean (Jensen Ackles) would die for each other. Dean practically raised Sam. One brother would sacrifice everything for the other, and that's what family's about: sacrifice. It's so intense watching the dynamic between the brothers. Yes, they fight. No, they don't always agree, but ultimately, they do what's right for their family, and that's what makes Supernatural one of the best shows I've ever seen.
I've been watching since I was 11, and this show never gave me nightmares. I don't curse just because Sam and Dean do. Yeah, they drink, but so what? At 11, it didn't bother me, and it still doesn't. While this show is not for the sensitive child (or teen; I have friends who can't watch it because it terrifies them), it's an excellent piece of television. Because I started watching it early, I'd say this show is okay for preteens who aren't easily scared.