We reported earlier that Twitterific, from Ikon Labs was a solid choice for a Twitter client. (if you don't know what Twitter is, please see the Twitterific post). However, Twinkle from Tapulous easily outdoes it from both a UI and features perspective.
iPhone and iPad apps tagged "Twitter app."
Twitterific is an excellent Twitter client for iPhone
Twitter is one of those new applications that either you "get" or you don't. Twitterers love the product for its ability to blast updates about your day to day life ("I'm at Starbucks, right now, getting a latte") to your friends, and basically anybody who cares to "track you".