I let my eldest daughter use my old iPhone, when I upgraded to the 3G, back when she was only 2 years old. Remarkably, she knew how to scroll through all the photos and knew how to get to YouTube. Her two favorite games at that time were Bubbles (bubble popping game) and BubbleFREE (bubblewrap emulator). She's now 4 and still uses it, but now she's got pre-school games like Monkey Preschool Lunchbox, Dora and Spongebob. I loaded Disney movies and some songs that she likes into the iPod app. I put family photos in the Photos app. She still loves YouTube, but knows it can only work in the house, under Wi-Fi. She knows how to use the camera to take pictures.
My other daughter who just turned two years old, will fight with her sister for use of said iPhone. So I threw on a case on my wife's old iPhone which had been resting peacefully all this time in its box in storage and let my youngest one use it as her own. I bought Griffin Woogies as well recently for them, since my youngest has a horrible habit of just leaving the iPhone and forgetting where it was abandoned. Now, you can't miss it, cuz it's embedded inside a huge stuffed, green sextapus case.
The one thing that has impressed me about iOS, even tho Android users keep saying how it's too easy and only dumb people use it, is that the OS is so simple and easy to use that even toddlers and pre-schoolers can use it! That is a good thing! I've never encountered a gadget where a baby can pick it up and start using it intuitively without instructions, yet be so powerful and all-encompassing with regards to its capabilities. This ease of use, alone is what got me hooked on the iPhone all four generations and can honestly say, I highly doubt I'd switch for anything out on the market. I love the iPhone and my kids love it!