A short list to help you...
Twitter clients have been around the Android Market since Android became a popular OS for mobile phones. Like every app store, it became crowded with different forms of apps to make use of this social media.
My main problem with Twitter clients is that they are becoming multifunctional. Let's take Tweetdeck for example. This app was mainly for Twitter, but the programmers decided to add functionality for Facebook. That way you should be able to see updates from both networks, in one screen. For the people who want every form of update in one screen this is a good thing, but for most people it is confusing. What was the next step? Add FourSquare to this app as well, so you would see more updates...
Why are developers adding more and more networks to an app? Is this to make people more addicted to their networks?
My choice for an Android powered Twitter client should be based on functionality and the speed of the app. You do not want to wait for updates and you want to see as much as possible in one screen. I chose the HTC Desire HD because of the big screen, just to see as much as possible.
Which apps are the best choice?
I will not make a complete list of the apps that are around, as you can find those yourself. Like I said, most clients support multiple networks and integrate those in 1 timeline, something that shouldn't be done. The following apps are better to solely track Twitter:
TwitterCredit: Android Market
Obviously, the client that is made by Twitter is one that should not be forgotten. It's timeline is straightforward and the search function is good enough. If you need an app that isn't too fancy, choose this one. Cons: No integration for websites like Twitpic, boring lay-out.
SeesmicCredit: Android Market
This was my favorite client for two years. It is pretty straightforward like the native app, but has support for multiple accounts. The main advantage for Seesmic is that it's fast! No fancy lay-out, just your Tweets. If you already love the Desktop version of this app (which is written in Silverlight and slow) will prefer this client for their Android phone. The downside is the boring lay-out and the minimal integration of websites like Twitpic
Credit: Android MarketTwicca
This one is last in line, but can be considered the best of three. A main advantage is that the layout is created in such a way that it will display as much as possible on one screen. For people who follow a lot of tweeps, this should be your choice. Compare this app to the other apps and you have an app that has integration for most websites, has an amazing look and has loads of plugins available in the Google Market