DestroyTwitter is a full-featured yet lightweight Adobe AIR twitter app. While many other AIR apps are guilty of being on the pudgy and/or sluggish side, DestroyTwitter is refreshingly responsive. Upon load it starts at about 40MB and after using it for a bit, searching, and loading a couple other columns it only climbed to 61MB. Very good for an AIR app!
Even though the memory footprint is light, it doesn't skimp on features. The app is maintained by Jonnie Hallman, an Experience Designer at Adobe, so that may have something to do with it.
Tweetings is a small, secure Twitter client for Windows. It has a compact interface that scoots out of the way when you minimize to the system tray.
Syrinx is a free, customizable twitter app for the Mac. It's interface is simple yet configurable. You can view a column at a time, either your friends, your @ mentions, or your DMs. Some key features:
TweetDeck is an Adobe AIR Twitter app for power users. Using a column layout, TweetDeck allows a user to set up many feeds at once. Some are specialized to Twitter, such as your friends, @ mentions, direct messages and so forth. But the real power lies in their numerous advanced search features, which filter the public timeline any way you desire: