Sometimes the question isn't what shows are appropriate for a 13 year old, but what shows are 13 year olds comfortable to watch with their parents.
I'm already an adult, and I turn down the Avenue Q OBC recording when I listen to it at home, and I have to leave the room out of awkwardness when watching movies like Scary Movie and Austin Powers (yes, really) with my parents. It's not so much what shows young people can handle, but what shows will freak out parents nonetheless.
Also, while Avenue Q can probably be enjoyed at face value (puppets! singing! porn!) by people probably 10+, it's deeper issues (racism in society, homophobia, problems with getting a Bachelors in English - heh-, etc.) is probably better appreciated by an older audience.
"It's not always about you!!!" (But if you think I'm referring to you anyway, then I probably am.)
"Good luck returning my ass!" - Wilhemina Slater
"This is my breakfast, lunch and f***ing dinner right here. I'm not even f***in' joking." - Colin Farrell