After the Twitter micro-blogging boom, several micro-blogging services started cropping up everywhere. However, despite the infamous Fail , Twitter seems to still be on top of its league.
On Linux, HowToForge presents two desktop Twitter clients, namely Twitux and and gtwitter. Whilst I have yet to try any of the two, I must say that both still lack the features that you get from the full Twitter web interface.
Personally, I use a Firefox plug-in, TwitterFox, for my Twitter needs on Linux.