Tweetcaster
After trying out many of the different apps available, I think Tweetcaster is the best for Android (I use a Motorola Xoom).
Well, what I actually like the best, much to my surprise after spending most of the past year tweeting primarily from my BlackBerry Official Twitter app (which, in my opinion, is the best Twitter app there is), is using the site with Google Chrome and some extensions. I love Slipstream and Hide the Guff, both of which have made the Twitter site and my stream much more readable.
Getting back to Android apps, Tweetcaster has the most aesthetically pleasing UI of the apps I've tried, and also the best functionality. Plume comes close, but the ads are weirdly placed in the free version of Plume, whereas in Tweetcaster, I find them almost unnoticeable. I like the multi-column side-to-side swipe layout of Tweetdeck, but I hate it's lack of functionality when it comes to managing lists, searching for people, or tweeting @ someone. Tweetcaster, like the BlackBerry app, suggest @s as you type, which I find immensely helpful. It's one of the #newtwitter changes I quite like (although on the site it's only the 500 most recently followed, whereas, to my knowledge, in the apps it's everyone you follow).
Anyway, I hope Twitter buying Tweetdeck is a good thing - I just want a Twitter app that has, say, all the current functionality of the BB app or Tweetcaster PLUS filters. After using Slipstrem in Chrome, I hate opening up any app for Twitter!