Recently a couple of friends got iPhone devices and asked me which ones are my essentials "must have" applications. This is my personal list.
Soundhound is a little application that records a song that is being played or singed in your vicinity and recognizes it so you can know the author and title.
Shazam does the same as Soundhound, but recognizes some songs that Soundhound fails to do.
Gowalla is a social application for locations. You can use it to leave note on where are you, interesting places you know, and see what places your friend have found.
Whatsapp is the ultimate instant messaging application. Contrary to normal instant messaging, it does not require any kind of login or registration, working just with the phone number, allows you to chat in any place, in any moment, with any of your contacts that also installed this application.
Viber is the voice equivalent of Whatsapp, allowing you to make voice calls over internet, absolutely free.
iBibliotecary is a must-have application for anyone that likes to read books. Allows you to keep track of what books you own, if you lean them, so on.
Facebook makes using Facebook easy on an iPhone, giving full access to everything on that social webpage (but their web applications) in a touch-friendly interface.
Twitter makes the same, but for the Twitter microblogging service.
Hipstamatic converts your iPhone's uber-powerful photo camera in a vintage toy camera with an almost infinite number of combinations, each with its unique effects.
iBooks is an eBook (or electronic book) store and reader, made by Apple and for Apple, with a pretty interface but a not so big collection of books (specially in other languages). Supports your own books in PDF and ePub formats.
Stanza is another eBook reader, that behaves a lot faster with PDFs.
Kindle is Amazon's eBook store and reader, offering a different (and sometimes bigger) catalog than iBooks.
Wattpad is an application that allows you to read self-published books, short-stories, poetry and so on.
TuneIn Radio allows you to hear in your iPhone thousand of internet radios of all genres and countries.
iRAE allows fast and easy access to the Real Academia de la Lengua Española dictionary.
Wikipedia allows the same, but for the free community-based encyclopedia of the same name.
The NASA application allows you to see the lastest space photos and news.
AppBox Pro is a swiss army knife of applications, making you have at hand dozens of little utilities, like a battery checker, a flashlight, so on.
GPS Lite allows you to see your exact coordinates as given by the integrated GPS module.
Dragon Dictation allows you to dictate to the iPhone and everything you say gets automatically converted to text.