As others have stated, we've found iPhone/iPad to be one of the kids (one is now 18 months and the other almost 3 year) favorite things to play with - from about 14 months or so they were able to unlock it and find their favorite apps or videos. We load it up with Sesame Street videos and some toddler games. They also love to look at photos and movies of themselves and the family. They also like drawing apps, music apps (Piano, Bloom, etc) The older one likes matching games - its helped them learn shapes, color, animals and animal sounds and now letters and words. The older one knows how to find videos on YouTube and Netflix already. (sigh)
Its saved us from numerous meltdowns when waiting in long lines or on long car rides. They also have to share it with each other.
A downside is that when the little one sees ANYTHING that resembles and icon, she taps on it as if it were an iThing -- she's done this on cereal boxes, books, TV screens etc.