AGirl's 3 years old and she loves playing games on the iPad. It really varies by day as to which app she plays with but some of her current favorites are:
Toca Nature :- She loves playing on this app and exploring the environment. This is one of her favorites that she keeps coming back to and playing.
ABC Gurus :- AGirl has never been into the alphabet apps even though I've bought a ton of them for her. This is the only app she has shown interest in and only recently. But for the last month, she has been consistently coming back to the app. You can color each letter and add eyes, mouth and various other features and activate it.
Little Builders :- This is an iOS Editor's choice app and I had just downloaded it because it had become free for the weekend. I had not really expected AGirl to get into this since she's not into trucks or building stuff but she really loved this app and has spent hours on it. At times, she would get frustrated because something she wants to do requires more finger control than she had at that point but the game is really good.