I am not a big fan of television in rooms. I do think that if a teenager does have good grades in school and good behavior, then a television can be considered. I would not allow cable television until a child is a lot older, around 15 or 16 years old.
As a professional who works in schools, it really bugs me when I am at a meeting regarding a child who has academic or behavior problems and find out there is a television in the child's room. When I am working with some of these children, they tell me how they can't fall asleep without the television on or they state if they can't sleep they will just get up and watch television - the one in their room. These are elementary age children. Often times, these children seem very tired in school. I honestly don't think most parents would allow this but it is sometimes very hard to know if your children are doing this if you don't have control over the television.
I do feel strongly that a child shouldn't have internet in their room. We will cross that bridge when we come to it as the world will be a completely different place then. Who knows what life will be like, technologically speaking, when my children are tweens or teens.
I feel that even having a video game system in the child's room could be a little dangerous - tempting. Video games are fun! If you have a child/teenager who is really into video games, it would be hard to fall asleep at night when you have easy access to the video game (...I just need to get beyond level 9)
Gosh, we just moved and now the computer is in our room. It is more difficult to just fall asleep without checking email/forums....the issue is temptation. Then again, my issue could be pregnancy insomnia