There are a whole raft of Twitter clients for mobile coming out and choosing the right one isn't always easy. Twibble is a pretty safe bet though, and offers enough to keep you in touch with what your Twitter buddies are up to.
Twibble allows you to follow people, post tweets, insert photos and links, and more. The application is also GPS-aware, so others are able to view exactly where you are in the world, and you can also track the location of your Twitter pals.
The Twibble UI is simple and clear, and can even be skinned (though at present there are only two themes). The set-up procedure is simple enough - you just need to enter your Twitter account details and click 'Save'. There are a few other tweaks you can make to your settings though if you want to customize Twibble a bit. For instance, you can tell the program how often to check Twitter, toggle vibrate mode, insert template text, and more.
Once you're up and running Twibble makes it very easy to view tweets. Besides just viewing them in list format you can easily open links from within a tweet, retweet messages (i.e. forward them), find users to follow, and much more. Of course, you don't get the same full experience that you have on Twitter.com and Twibble doesn't display profile picture icons or allow you to view full user profiles. Of course, getting addicted to following Twitter on your phone can be a costly thing if you don't have a cheap data plan. Luckily, Twibble tries to keep the amount of data used to a minimum and will only download new tweets. According to the developer, these are normally transmitted in compressed gzip format to really minimize file size.
If you're looking for a simple, no-nonsense mobile Twitter client, then Twibble is well worth a look.