Twitter is all the rage these days and I've been using one of the more popular desktop Twitter applications - TweetDeck http://www.tweetdeck.com. TweetDeck runs on top of Adobe AIR - http://www.adobe.com/products/air/.

My day-to-day OS on my workstation is Linux (Fedora 10 to be exact). I installed Adobe AIR and TweetDeck with no issues on the initial installation.