Now you dont need to open twitter always to view the tweets. Chitter.im is a Google Bot which allows you to combine Twitter and Gtalk and you can easily tweet, retweet, quote, follow, unfollow and send direct mail to your followers and friends. This Bot integrates Twitter app in your Gtalk.
To do this visit the site http://chitterim.appspot.com and authorize your gmail and twitter account and add firstname.lastname@example.org as a friend in your Gtalk thats it. Now you will receive all your twitter tweets in your GTalk.
To get the Help about any topic just send an IM to email@example.com as /h, and it will show the help box.