Tweetdeck or Seismic Desktop are two big ones that people like to use. Tweetdeck has several good features but IMO tends to use quite a bit of memory and bandwidth (unless you turn off the automatic update option.)
There are also gadgets you can add and use directly from Firefox or Google. One is Twitterfox and I'm sure a quick search on google will help you find their gadget.
Here is a fairly helpful post on 27 top Twitter applications
and here is a post from Mashable that compares 19 different Twitter desktop applications
including the two that I mentioned above.