I have a 4 month old girl, and I've already been exposing her to the iPhone (since she was 2 months old, actually). I have a Baby Einstein DVD and Monsters Inc. loaded on the phone. It's a terrific pacifier when she gets ansy while we're out and about. Most of the time, as soon as I turn it on, the cries stop and she becomes transfixed by it. Of course, I have to sit there and hold it in front of her, but it works. Brief disclaimer: I don't use it to replace tending to her needs, but if she is fed and changed, but still just needs something to occupy her, it works terrific. It is also a good distraction if she has a tummy ache or runny nose and just needs something to take her mind off of it.
As for Apps, Bloom is great for infants. I turn it on, set the delay to max, and hold it close to her hand. If she's in the right mood, she'll swipe at the screen which plays the notes and colorful graphics. She loves it. Koi pond is another good one.
I have also played tunes on Ocarina for her a few times. I've had limited success pacifying her with the White Noise program, and I have some Baby Mozart music loaded as well.