I let my kids play. My 16 month old isn't very interested, but my 3 year old really likes it. They don't play every day - maybe just one or two times a week, and never more than for about 30 min or so... We have a lot of educational games and I think it's been a positive thing for them. It's a good distraction in some situations (like if we have a family dinner which is out and takes a long time and is past their bedtime), and is great for things like planes etc when they can't run around. I think as long as it's in moderation, it can be a good thing. But I can see how it could easily get out of control as well.
All that said, I have a smartphone and I have determined NOT to put ANY kids apps on it, because I know that if I did, and if my kids knew that they could play on it, they would ALWAYS want it and it would probably end up being a negative thing. My phone is JUST for me.