I just recently started using the TweetDeck web app for Google Chrome. I absolutely love it. I used to use TwitterGadget on iGoogle at school and the Twitter web site at home. (Twitter is blocked at school...argh!). Luckily both of these apps get to Twitter in a round-about way.
I have my TweetDeck set up with my Inbox on the left, Home in the middle, and Me on the right. I can not set up Facebook on here, which is fine because I don't use it much for school things.
One of the features I really like is the fact that when you reply to someone, it shows that Tweet below and you can easily see the conversation. Seeing all three items (inbox, stream, and mentions) on one screen also makes it easier to keep up with what's going on.
If you use Twitter, I highly recommend TweetDeck. There is the web app and a desktop app available, as well as apps for iPhone, iPad, and Android. (I use Twee on my Palm Pre+ which I really like).