Developer: Ubermedia, Inc.
Price: free Download on the App Store
TwitterFon, by Japanese developer Kazuho Okui is, in the author's own words "a simple and fast Twitter client for your iPhone". Unlike other apps such as Twinkle, it has a plain, simple background, and really tries to stick to the basics - no geo social networking, no ability to "broadcast your location" - just a clean, simple Twitter interface.
More apps should try to copy the TwitterFon formula and emphasize design and functionality over features. TwitterFon is truly a pleasure to use: it's clear that the developers have spent considerable time and energy trying to build the perfect, minimalist twitter client - without getting tempted by extraneous features such as the ability to see "nearby" users.
One feature that the app has which I find incredibly usefull is the search tab which allows you to query the "TwitterVerse" for tweets on any particular subject. This is something even the twitter web site doesn't do and is certainly not available in apps like Twinkle, and will cost you $3.99 from Tapulous's other twitter app, Tweetsville.