One concern that people often have is: If I were to let my child do whatever he wants, he would sit and play video games/watch tv/play all day.
First of all, I maintain (and research backs me up) that "play" is one of the most valuable activities that a child can be involved in. It has emotional, social, cognitive and intellectual benefits. (I actually did make that point in my speech.)
But let's say your kid wants to sit and be on multimedia all day.
1. This may just be an extreme phase of finally being allowed the freedom to play/watch what is very desirable, and after a bunch of months, the child will moderate out and do more activities.
This happened to my oldest daughter. I used to be very strict, and when I finally let her, it took 10 months until she was willing to go out and play with others, or go to the park, or to the beach. At around 8 months I began to seriously panic and fear that she would do nothing but watch TV for the rest of her life. Then one day, she emerged back into life and is a moderate (towards infrequent) user of internet and TV.
(I must note that if a child is only interested in video games for years, it might be a sign that real life is stressful or not as enjoyable as virtual life, and steps should be taken to address real life and make it less stressful and more enjoyable, whether via therapy or by restructuring real life.)
2. It may be that whatever your child is involved in is having a deep and profound impact on her understanding of the world and she is learning something extremely important.
I have seen this (I did mention this point in my speech, too) with my second daughter who spent many hours rewinding and scrutinizing particular scenes in TV shows and movies and is currently involved in animation, which has subtle facial expressions and movements and interesting dialogue. I had no idea why she was doing what she was doing for so many hours and over and over, and I am so glad I didn't stop her because her brain was LEARNING something very important and very fascinating to her.
My son also gets very involved in mastering certain video games or in doing certain activities online. Usually it coincides with some cognitive development he is working on. I prefer to get out of my kids' ways and let them proceed. Their brains know what they are looking for and how to learn it.
BUT, getting to the point I forgot to make: I saw a Supernanny episode once where the parents insisted that their children would only eat chicken nuggets, wacky macs, fast food, and junk food. They said their children refused to eat anything else. Supernanny was trying to tell them that the children's behavior and health was being affected by their diets. (Personally, I had some sympathy with those parents, having done the "pizza bagel/fish stick/wacky mac" weekly menu phase numerous times.)
Supernanny brought the children to the grocery store. She introduced them to the produce section, in all its multicolored glory. The children gazed at it. They were astonished. She encouraged them to look closely, to wander through it, to choose what they think they might like to eat. They chose peppers and green beans and plums and peaches and peas and melons and berries and beets and a spaghetti squash and more-- a cornucopia of fruits and veggies. Then they went home and the kids helped cook some of them and ate some of them plain. The children enjoyed some and didn't so much like some. Many they loved and put on the grocery list for next week.
A big part of unschooling is going out into the world and exploring. Introducing your children to all sorts of things they wouldn't have access to or time for. Who knows what they will love.