(updated July 13, 2015)

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This just may be my all time favorite app. It tracks feedings, pumping, sleep, medical records, and everything else that you would expect from a tracking app. The interface is great and it is really intuitive. It also allows you to effortlessly make an adorable PDF baby book of the first year (I started the book when I was still in the hospital). Just modify your pictures to make them square before putting them in the app, otherwise they get distorted. I also used the Sprout pregnancy app and loved it, which is why I decided to try the baby app even though there were no reviews at the time.
In case my saying so isn't enough, the app has been named a TIME.COM Top App, recommended by Consumer Reports, and named #1 Pregnancy App by BABBLE.COM
There is also a Sprout Baby+ for iPad app, which should be available to you for free if you already have the iPhone app

Based on your baby’s due date, this app (IOS) (available for Android too tells you when your baby will go through developmental leaps, which are accompanied or preceded by “stormy” periods. When S was inconsolable, this gave me comfort that it was only due to a temporary and normal developmental advancement. It is great in the beginning, later on the timeframes spread out so it becomes less useful. For example, the first leap happens between weeks 4.5 and 5.5 and the 7th leap happens between weeks 41.5 and 46.5.

White Noise ™

I like Pink Noise option within the app to help baby sleep. There are many apps like this, but this one worked for me. I repurposed an old iPhone as a noise machine. I keep it on airplane mode (to limit baby's exposure to radiation) and it goes wherever the baby goes.

Songs that made my baby stop crying
- John Legend's All of Me (I must have heard it 1,000 times). Especially when S is overtired, almost without fail, this song makes him stop crying. Once he is quiet, I switch to Pink Noise and he is out like a light. At six months, S is such a happy baby and barely cries, but when he does this still works!
- Doris Day - Bushel and a Peck. This worked when S was just a few weeks old. Every time I put it on it caught his attention.

Cloud b On The Go Travel Sound Machine Soother, Sleep Sheep for the stroller
- People love this. I thought it was great until I discovered Pink Noise. The issue with this product is that it shuts off after 45 minutes and it isn't quite loud enough.
Yoga/Exercise Ball
- When all else fails, try bouncing your fussy newborn on a yoga ball.
- sometimes the only way to calm a baby. I have this one - - it is good and the silvery grey is nice, but it doesn’t come with a pump. I used my bike pump.

Projector
- My son likes the Le Petit Prince "Touch Active, Easy Clean" Twilight Constellation Projector Night Light. I chose this one because I was afraid that a projector with moving images would be too stimulating for night. He was mesmerized by it for at least a month and it signaled to him that it is time for sleep. He isn’t as fascinated by it anymore, but it still works as a sleep cue. Also, if he is fussy at bedtime, I spin it. This catches his attention and calms him.

Lovie

At my son's four month visit, the pediatrician OK'd him sleeping with a lovie. That very night I gave him one of the Angel Dear Pair and a Spare Lovies that I had gotten as a gift. He instantly took to it, smushing it all over his face and soothing himself to sleep. What is great about the Angel Dear Pair and a Spare Lovies is that they come as a pack of three so you can always have one handy. If you prefer cotton Lovies, check out these Under the Nile organic lovies). Whatever lovie you get, make sure it is machine washable.