My son is 3-years-old and he rarely watches TV at our house. We don't have cartoon channels and he hasn't shown a huge interest in any of the cartoons he has seen. When he's at his grandparents' house for a day on the weekends, I know he watches at least 2 hours of TV/day. He watches his favorite Japanese superhero cartoon and then he watches usually an educational phonics DVD before bed. Their TV is always on. But, at home we're not big into TV.
I would say maybe once or twice a week I let my son sit down and watch Word World or Curious George on PBS.com. I have Kipper DVD that he watches sometimes. If he watches a cartoon for a solid hour, to me that is plenty. And he doesn't do this every day. When he plays games on PBS.com online, usually I'm nearby monitoring him or helping him with it. He rarely does this. The great thing about Word World and Kipper is that each episode is no more than 15 minutes so he doesn't need to watch a full hour in order to enjoy a fun story. Sometimes when I'm trying to get something done, I'll let him watch 4 or 5 episodes in a row but that's not often.
So, if my child was having 3 hours of "screen time" every day, I would personally feel that was excessive. I would much rather that he be involved in making something with his hands or playing in another way. I picked up some very interesting workbooks from a discount book store in the TST East Station for $10 HKD/each that have stickers and games for different areas including math, reading, writing and phonics. He really enjoyed doing a few pages in those and for me to help him with some. The nice thing is that unlike doing something online, after he's done he has something to show or display about his work which makes him feel really proud and we hang his work up in his room. But, my son is a bit odd in that he LOVES to do homework and gets excited to do his assignments from kindergarten and asks for extra work from me.
We don't have an iPad but if we did I would really limit his time on that as well. That's just how we do things.