The first Mac app I downloaded this morning after finishing the update to Mac OS X 10.6.6 was Twitter for Mac 2.0. This is the app formerly named Tweetie, and it's a free download from the Mac App Store.
If you have previously used another Twitter client on your Mac, or if you're currently using the eponymous Twitter app on iOS, then you're going to want to at least give Twitter for Mac a try. Here's how to get Twitter from the App Store. Note that you must be running 10.6.6 on an Intel Mac to use this app.