Android (4.0+): Not to be confused with the backup utility with the same name, this Carbon is a brand new Twitter client. It sports a minimalist UI, and it expands photos and media for easy viewing.
WebOS users may remember Carbon being plagued with development delays, but it has finally been released for Android. The app brings lots of one-handed gestures, it supports multiple Twitter accounts, and it doesn't clutter your stream with too much information.
Photos and video screencaps are automatically expanded in your stream for you, and you can tap them to enlarge them or open them in another application. The menu button gives you quick access to your favourites, lists, trending topics, search and personal filters, where you can customise your stream to omit certain applications, Twitter users, keywords or hashtags.
Tap any tweet to get a larger view, or swipe right to left to browse your mentions and direct messages. Drag down at the top of your stream to refresh. Those swiping gestures work on almost any screen, by the way -- if you're viewing a tweet, swipe from the bottom up to see replies to it, or right to left to go back to the main stream. The same applies when you're browsing profiles or lists: most things you want to do are a gesture away.
It's not perfect though: some features are hard to find, there is no tablet support yet, and it's lacking a homescreen widget. If you're not in love with your current Twitter client, it's worth trying. It's free and available now at Google Play for Android 4.0+ phones.