I love Twitter but when I use my Linux laptop (Ubuntu running Hardy Heron) I don’t have many native options for Twitter clients. The preferred native client appears to be Twitux. Though the nascent client is a little primitive for me. Another popular choice is gTwitter though in my experience it’s only been marginally better.
On Mac OS X I prefer Twhirl which allows me to send tweets to separate accounts from individual windows. So I can send tweets for my @zenoss and @mrhinkle accounts. Twhirl is an Adobe Air application which now is available for Linux as an alpha. Thanks to Seth Yates I now have Twhirl running as an AIR application with Adobe Air running natively on Ubuntu. the only downside seems to be that the notification windows are a little “flutterly” I really don’t care for them anyhow so I turned them off and everything seems to run well.