No, we don't have screen time limits in our house and while Princess does spend her fair share of time playing video games and watching TV and movies, she spends lots of time with other things as well. It is all up to her. Yes, there have been times that I've worried a about the amount of screen time. The more I focused on it, the more screen time there was. But it seems that as soon as I let it go, so does she.
The thing I needed to learn was that even when she does spend all day with a screen, she is still learning. Colleen over at The New Unschooler (who isn't so new anymore) recommended Don't Bother Me Mom--I'm Learning. It was a huge eye opener. I have always been very open about screen time but this book helped me see all the amazing benefits.