I agree with previous posters who say that you need to find what works for your own family and what you want for your own children, and then to be confident about your own choices. Then, of course, you will probably need to reevaluate your choices now and then as the children grow older.
We have chosen to be more restrictive in these matters than most of the families we know. We have a family iPad and my DS who is 8,5 is allowed to play games on it 2 hours per week, usually Fifa14 or Minecraft (no shooting games). DD who is 5,5 uses it perhaps one hour per week. In addition to this, they sometimes watch Netflix on it together, although rarely amounting to more than an hour or two per week. Also, I have recently taught DS how to make Lego stop motion films, and, of course, he is allowed to look things up on the internet (but then always asks first and I usually need to help with spelling etc).
This is the reasoning behind the balance we have reached for our family:
A family iPad rather than everyone having their own device makes it easier for us to manage screen time. We will probably reevaluate this in a year or so. I don't know how many times we have visited friends where the host children don't bother to get up to greet their guests, as they are too immersed in their screens. I find that a bit frightening, but obviously it's not the fact that they have their own screens that produces this behaviour, but rather which rules are in place.
We do want our DS (and eventually our DD) to feel comfortable socially, ie to be used to the same games that his friends play, so we are happy to show interest/download new games that he talks about, provided they are age appropriate and not violent. As far as I can see, there is no social difference among peers whether you play Fifa14 or Minecraft for 2 or say 10 hours/week. Also, I can't for the life of me imagine what skills those extra daily hours of gaming would give him?
We don't want our children to get used to instant gratification (ie as soon as you are bored, you ask to go on the iPad, which is what we see in loads of DSs friends whose parents have less restrictive/no rules in place.) We want them to develop the ability to entertain themselves in other ways. Many posters here talk about how their children are perfectly able to both spend hours on electronic devices and still be very creative and active. I can only congratulate them, but in my experience there is a direct (negative) correlation between screen time and the ability to entertain yourself. For example, my son is turning into an avid reader and gets a lot of enjoyment out of this. This is also reflected in his creative writing in school etc.
However, if his screen time wasn't limited, he would choose playing games on the iPad over reading, precisely because of the instant gratification factor. He is not old enough to make that choice for himself. And, to me, learning to concentrate on and understand longer, slower texts will be of much more use to him in school than being able to navigate on an iPad. A little judgey here, but I think our whole society is more than a little deluded in overestimating the importance of acquiring technology skills at a young age, while forgetting the skills that risk getting lost along the way.
We have also noticed that when we have had less restrictions in place, he not only doesn't read or draw or play with his sister, he is also generally in a bad mood. So the fact that "he loves going on the iPad" is not, in my mind, a good enough reason for him to do that as much as he wants to (just as I wouldn't give him unlimited access to sweets just because he likes them).
"It keeps them quiet" is never (in our family) a good reason for just handing over an electronic device. Also, I personally believe that we would be doing our children a disfavour if we didn't teach them how to manage the fact that life can be boring sometimes, as in waiting for your meal in a restaurant, waiting for an appointment etc. These minutes do not necessarily need to be filled with entertainment, on the contrary (again, not judging others, just what I want for my own children). I can just see how neurotic I am myself in constantly checking my phone as soon as I have a spare moment (although I try to be out of sight to not set a bad example...), I hope to postpone or avoid that for my children.
Sorry about long post, it's just something I've thought a lot about...