I'm very torn about this and I am probably going to get a full on roasting but we don't limit screen time in our house at all. We have no rules about it, which is probably not the best way to approach things but my philosopy is that if I ban something it makes it so much more attractive than if I just arrange life so that there isn't a great deal of time to spend in front of a screen.
My girls both have very full after school schedules. They have activities on Mon, Tues, Thurs, Fri and Saturday. They are free on Wednesday afternoons which are spent doing music practice and any homework that wasn't done on Saturday after which they may do whatever they choose.
Sundays are family time, we often do spend the afternoon watching a movie together on the couch whilst munching popcorn but we are also often out on Sundays. We have also been known to spend an hour on Saturday evening enjoying Strictly together!
Saturday morning is usually the time where they spend the most time on their screens as it's the day that I would like to catch up on my sleep having been up at 5:30 every morning during the week however once they've had breakfast it's homework time and then off to ballet and then home for more homework and music practice!
I haven't worked out how much screen time they get a week, perhaps I should because it's likely to be far more than I would like it to be.
We have google safe search enabled on all our devices as well as YouTube safe (prevents all those inappropriate comments from appearing) but my girls almost never use YouTube. My eldest dd uses the computer mostly to search for stuff on Amazon that she would like to buy and also to modify her website. She is also "writing" a book so she uses the pc for that quite a bit.
My youngest is more of a fan of minecraft and of Sky Go so that's what she does with her screen time. She also likes Google Earth and spends a good amount of time studying various parts of the planet using Google Earth. She likes to do research on topics that they are covering at school so she will look up things that she finds interesting. My feeling is that not all screen time is "bad" time.
Having said this, I now realise that my children are both total geeks!
My eldest would far rather read a book than anything else. Sometimes on a Wednesday, my girls will settle down in a bedroom upstairs and watch a movie together on one of their ipads. Luckily they have the same taste in movies (schmaltzy Disney animal movies) although Mary Poppins and Annie have lately taken their fancy.
My children seem to get bored with things if they are allowed to do them all day so they choose to fill their time with a variety of activities. Sometimes it will be a game of basketball outside or playing on the climbing frame and sometimes it will be a movie indoors or building a whole world in minecraft!
Interesting topic... maybe I should count up how much time they are spending on screens and start limiting it...