TweetDeck is one of the world's most popular Twitter clients. His popularity comes from its efficiency and ease of use. It is for me the best Twitter client I have ever used. It comes with a dark interface, just perfect for the eyes. You can add many columns, started from your timeline, replies, dm's, public timeline and even columns with searches (you can view constantly what people from all over the world are saying about something).
I'm using it almost everywhere. On my computer (Linux), on my Windows-based Laptop, on my MacBook, and even on my iPhone !! Its installation will also install Adobe AIR, which will practically manage TweetDeck. But when you're using TweetDeck, do not use any other Twitter client at the same time. Both clients might search periodically for updates, and the requests limit per hour will be passed, so you will have to wait for them to reset in order to receive new tweets. And it can connect even to your Facebook, MySpace, or/and LinkedIn simultaneously, and get updates from this networks.
Just try it, I'm sure you'll like it: http://www.tweetdeck.com/.