Authored by Iain Dodsworth, TweetDeck (available here), could give other AIR options, like Twhirl and Feedalizer some new competition. While I'm not typically a huge fan of AIR apps, I found TweetDeck to offer a great number of customizations that have me keeping it open and on the desktop around the clock.
The TweetDeck Interface (Click for Larger Image)
TweetDeck offers four major columns in which to organize Twitter data: "All Tweets", essentially your friends' timeline, "Replies", showing replies to you, the equivalent of Twitter's replies tab, "Search", which will keep a running search window open for a term you've selected, and "Group", which lets you make a sub-set of those you follow on Twitter, and make a miniature timeline.
You can also, of course, post your own Tweets from within the app, just by hitting the "Tweet" button at the top and entering what you want to say. TweetDeck counts down the number of characters to make sure you don't exceed 140.
The recent strain at Twitter has resulted in the service reducing the number of API calls developers can make to get Twitter updates, and there, TweetDeck has you covered as well, so you learn if there's any slowness, where to lay the blame.
In addition to the integrated search functionality, I was most impressed by the grouping function. I was able to create a group called "Lady Digerati", and could hand-pick which Tweeters would be followed, including @corvida, @sarahintampa, @veronica, @TheMacMommy, @NicoleSimon and others. You could, of course, make your own sub-groups to get a different subset.
While Jesse Stay and others have said Twitter's major issues have decimated the developer community's efforts around Twitter, there are still some looking to innovate, TweetDeck being a good example. Of course, given it's early status, there might be some issues, but it's worth taking a look, as the application has some great potential.