Hi, Dolores!
Congratulations on considering Disney Cruise Line for your family's vacation! In short, my two oldest (16 & 13) would give you a resounding "Yes!"
On all of Disney's ships, there are entertainment and activity choices to meet every age and stage of life...most especially teens. Teens can enjoy music, movies, video games and other teen-only activities inside Aloft (ages 13-17) on the Disney Wonder, The Stack (ages 14-17) on the Disney Magic or Vibe (ages 14-17) on the Disney Dream. All have big-screen plasma TVs, a lounge area, dance floor and Internet café. Teens have plenty of freedom on a Disney cruise under the watchful eyes of trained counselors. Teens can see "What's Happening Today" in the Personal Navigator. There are also teen-only excursions on Castaway Cay, Disney's very own private island paradise.
Also, click
here to see the Onboard Activities Search which I filtered just for teens -- you can see that there's so much to do on the ship that it makes it hard to convince the kids to come see the sights in the ports of call! I hope this helps you plan.
Have a wonderful day and a magical vacation. Bon voyage!
Andi