For working: WhatTasks is the most used app I have. No more post-its, no more todos in kaos! It follows the GTD idea. Buy the full version, it is really worth the money. Then, something classic: an English-Italian dictionary form Wordreference, the Google Mobile app for my Google addiction, Nimbuzz mobile for chatting and Voiping (especially Skype). Finally, Ultimate Voice Recording for voice recording: it is really flexible and customizable, unlike other apps available for iPhone. I travel a lot with trains, so iRail is also useful for me. Stanza transforms your iPhone in an eBook reader: please, tell me how to integrate PDFs in the comment, I need it!
For social networking: Pixelpipe is really great: you get your photos in your social networks very easily, as Ping.fm does for textual microblogging (unfortunately, not integrated, but luckily the web site works well on iPhone Safari). Facebook and WordPress do what you expect, no more, no less.
Finally, some games: I love go, so I got iGo, which is at least good as cGoban and the like, Labirinth, Tetris and PacMan are classics, Zoom Zoom is for my child, who loves cars (it does not need any touch of the iPhone, so it is allowed by my personal strict policy…). But the most insteresting ones are made by Brian Eno: Bloom is an incredible way to play music, my children really love it, while Oblique is the porting of a classic card game by Eno of the 1970s – in truth, a set of koans.