Blackberry has its own Twitter App which is much improved with the latest leaked version. Supposedly it is to be officially released any day now.
The latest version is much faster, scrolls better, and allows you to set the font which is great for some. Also when you have a new tweet can you set it to notify you in the message list. The app is not as advanced as the some of the third party ones like UberTwitter but I do like the simplicity of it. I have links below to the third party offerings.
What's interesting to me about Twitter is if you set it up right, you get first hand news of interest. For example, I follow pro cycling. Check out Lance Armstrong's tweet as he gets ready for the rainy Tour of Flanders on Easter Morning 2010.
On the home page you can see your Tweets, with small avatar pictures as well as small thumbnails of linked images.
You can see your own profile.
You can also see your Mentions, Direct Messages, Find People, Search and find Popular Topics. Overall I really like the simplicity of the RIM Twitter Client.
Here is a view of the notifications in the message list. When you click on the message the Twitter App opens. I love this feature.
Current shortcuts -
Alt+5 (find people)
Alt+7 (popular topics)
New features in 22.214.171.124
Other Alternative Twitter for Blackberry Applications include:
SocialScope still in beta but see shots here.
UberTwitter which I also use and like - lacks the message list integration which I find nice.
and for a story on all of them from Crackberry go here.
Yet for sure the biggest news is TweekDeck is working on a BB app. I love their desktop app.