I've been an iPhone owner for the past 2 or so years. I've tried a bootyload of apps for various different things. But here are the ones that I just cannot live without.
I prefer this Twitter app over many others simply because it lets me post to Twitter and Facebook at the same time. I have Echofon and Twitterific on there too, but those don't have that dual posting I like, so they don't get as much use.
I don't remember the last time I called an actual cab base to get a cab. Way2Ride is so simple to use, and the accuracy of where the driver is, and how long they'll take to get to you is amazing. I stopped using Uber for this app.
This is app is pure GOLD for me living in New York City. It tells you which buses and trains are near you, and give PERFECT real-time updates on how long transportation will get to you. It's one of my most used apps (I live in NYC and don't drive, it's the norm here), and I love it to pieces.
The native iPhone email app is fine, I guess. But I always felt so overwhelmed when all of my inboxes got filled up, so I looked for an alternative. The Gmail app is great cause it automatically sorts your mail into separate folders, making it easier to go through all of them.
This app is great for on the go quick photo editing. I also have it on my iPad. It has simple things like crop and resize, but it also has filters, lets you freehand draw, and a few stickers and emojis in there as well.