Here is a list of the iPhone and iPad apps for babies

They are all very basic in operation, with the only interaction required being to touch the screen, which makes them ideal for babies or young children with no previous experience of touch screen interaction.

1. BabyTap – 42 LLC

and

BabyTap HD – 42 LLC

A very simple app – each time your baby taps the screen a different shape appears where they have tapped, accompanied by a sound. Great first app. You can make some configuration changes in your iPad Settings section.

2. Baby’s Musical Hands – Streaming Colour Studios

Puts coloured squares all over your device’s screen. Yellow squares make piano sounds, blue squares play guitar notes and red squares (iPad only) make percussion noises. Stars appear when your baby touches the screen, enabling them to make the association between the touch and the noise.

3. Baby Explorer – Emantras Inc

Turn your iPad into an activity centre. Lots of buttons to press, and this app also introduces the swipe action as well. This app has a long life potential as it appeals to toddlers as well.

4. Peekaboo: Ladybird Baby Touch – Penguin Book

5.  Happy Babies: Ladybird Baby Touch – Penguin Books

Based on the print books by Ladybird, each app features four different sequences. After a small animation, the app pauses until baby taps the screen to advance. Lovely bright colours and British narration make these apps distinctive.

source: http://www.geekmummy.com/favourite-baby-apps/