After the Twitter micro-blogging boom, several micro-blogging services started cropping up everywhere. However, despite the infamous Fail whale, 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.
One word: Gwibber. It makes all other clients look retarded. AND it can go across multiple microblogging networks….facebook, twitter, identi.ca, pownce, etc.