If I have to choose one among all of the Apps, without a doubt I will tell you....it's gonna be the Twitter App!
You know what? You can download from iTunes store for free for thie Twitter application (Or you can try download Echofon (It's free too!) which is also one of the Twitter Apps but I'll prefer Twitter Apps though.)
I'll tell you that, Twitter is the Newspaper for today! This is why I will say that this is my favourite application because everyday, if you sign in into your twitter account, you'll know what's happening around the world (Of course you'll need to follow someone first)!!!
Twitter is really cool in the sense that you can follow up different person or even news channel to get updates from them! For me, I would recommend you to follow CNN news, OMG facts and some of your local news channel on twitter so that you can get updates on what happening around the worlds and some fun facts everyday (You can save your money and time to go out and buy a newspaper but just tapping your iPhone 4 screen using this Twitter apps)!
Of course, you can follow your favourite celebrities or athletes on Twitter too to see what's they up to lately. Just make sure that it is an official account or verified account!! Like me, I'm following Keith Urban and Bon Jovi (Yes, I just mention them again!!!) so that I'll get their latest and exclusive news on them!!! There are lots more you can follow on twitter though. As a science student, I'll follow up some science channel as well.
Besides that, you can interact with peoples from all over the world, knowing how is their culture and what happening on their country by checking out their daily updates and interaction with them on twitter. Since it is a micro-blogging website, you can update your daily activity as a more easier version of blogging too!!
Besides that with this Twitter apps on hands, you can tweet wherever you like and check out latest info or news in a more convenient way. I just wanna say that Twitter is a really useful and convenient website and with the released of iPhone 4 and the twitter apps make it more convenient for us.
(PS : I'm really appreciate the invention of iPhone apps!! They are really useful!!!)