I've been using one called Twhirl for a long time now, but I think I need to find a replacement.
I just discovered a missing feature: support for retweets. It does support them, but it actually hasn't been updated since Twitter added support for retweets. So before, you would have to copy and paste the message and add something like "RT @yourmom" to the beginning. So this client does that automatically, but it doesn't show up as an actual retweet on Twitter.com. The reason this matters, is that I often enter contests over Twitter that ask you to retweet something, and if mine aren't showing up as Retweets, I bet I have no chance of actually winning.
What I like about this client is that it sits in my system tray and pops up a little notification when I get a tweet, and makes a sound. That way it's hidden unless I'm getting a tweet. I've tried TweetDeck, but it seems to lack the notification features that Twhirl has, and just seems to lack options in general.
Can anyone recommend anything else?