You can add friends, to see what they are doing, or people like Leo LaPorte, Robert Scoble, Chris Pirillo and Darth Vader.
You have the option to make your "tweets" private, so only invited friends see them. Which reminds me, I need to invite more of my friends to it, although many of them aren't geeky enough to want to use it.
This past weekend, I noticed that Leo (via Twitter of course) was going to do an episode of This Week In Tech, on TalkShoe, and when I joined, it seemed they were all talking about Twitter there, especially a mashup of Google Maps and Twitter called TwitterVision, which maps where people are twittering from. It's kinda cool in away, and reminded me of the Twitter screens I'd seen on Flickr taken at SXSW last week.
It really does seem to have taken over the net recently. I was listening to the latest podcast from MajorNelson, and he mentioned it as well.
What's next for Twitter?