There are a host of Twitter clients available for the iPhone, and I’ve tried a lot of them, including Twitterific, Twittelator, Echofon, and Twitter's own native app. However, none of them really clicked, and then I started using Tapbots’ Tweetbot.
I loved the little tweaks and flourishes in the interface, such as the smart gestures and yes, even the sound effects (which are subtle and add to the “weight” of the app), as well as its customizable interface and compatibility with a number of external services such as Pinboard.
Version 2.0 of the app appeared in the App Store earlier today as a free upgrade. It has a number of updates, such as an updated timeline view. My favorite feature so far is the built-in Readability view, which strips the layout, ads, etc., from external links and presents them in a much cleaner and more, um, readable format.