It's been two years now since I'm using the iPhone and I still love it. I must admin, I was a Nokia fan for a very long time, but ever since I got that iPhone 4, I've changed my view regarding the cell phone world. If you ever had an iPhone, you now what I'm talking about here: there is something more catchy and more magnetic like the iPhone. It make us want to use it just for the sake of using it. Even music sounds better on the iPhone (as I said, I'm biased!). That's why I'm going to share some interesting apps that you can use when you have spare time to lose. I will group them by resemblance and importance. This is a personal top, and may not resonate with your needs.
Yahoo Mail and Gmail App
These apps are free in Apple Store and they are really handy, especially if you want a cool interface. For me, they are a life savior because I have an Internet plan that's wap-based and does not allow me to use mail protocols. So, the default mail app is working only when I'm on WiFi. But with these apps, I can read my mails flawlessly.
WhatsApp, Skype and Facebook
It's really important to stay connected with friends. That's why I'm using these apps. They are in no particular order, because I use different apps to talk to different people. I'm using WhatsApp to talk with some of my work-colleagues and friends that don't use Facebook. I was lucky to find WhatsApp for free in Apple Store thanks to a promotion that was taking place that day. I use Facebook just to stay connected with all the people I know, and I use Skype to talk to close friends, family and sometimes I use it for work.
Mercury, Safari, Chrome, Dolphin, Opera
I know, I use many browsers. There is a reason for this. I have various accounts on various websites, and I don't want to mix everything together. This way, things remain independently. I use Mercury as my default Internet Browser, because it has many features and because there is something cool about its Reader option. Dolphin is also really cool, and Safari is pretty fast.
This is probably the best News App I've ever seen on iOS. Maybe I'm just biased, but in addition to its own news (which are awesome), it allows you to add content from practically every platform you can think of (Twitter, Facebook, Reddit, Feeds). Whenever I have few minutes for myself, I just browser the news. It features a nice way of scrolling the news. I'm usually into tech and science, and there is plenty of content for me there. I recommend.
Camera+ and Camera
For me, Camera+ is probably the best photo app you'll find on Apple Store. It's not free, but it's a must if you like to take cool photos with your iPhone and edit them later. As a second foto app, I will probably recommend iOS native app. I'm using Camera mostly when I need to take a quick photo. It's really fast.
Other social apps
As you can imagine, I have accounts on every social network out there (Twitter, Wordpress, Pinterest, Reddit, Stumbleupon...), that's why I have an app installed for every each one of these accounts. To be true with you, I'm not using them that much, but it's really useful to have them installed in case something happens and I need to use them.