It seems like Twitter is a love-it-or-hate-it thing for a lot of people. Some people can't understand why others feel a need to carry their cell phones around and text things like "Ham Sammich for lunch" or "I just put on deodorant" every few minutes. Other people see real value in Twitter, and use it to keep in touch with people they might not otherwise talk to as often.
Personally, I'm so damn plugged into the internet with all my RSS feeds that I often have lots of stuff I want to share with the intarwebs, but it's not always quite enough to warrant a blog entry. If it's less than 140 characters, I can tweet it. It just doesn't make sense to me to blog about getting Rickrolled while trying to watch the new Terminator trailer or the car I saw changing lanes into another car while driving to work, but these things work great in 140-character format.
Twitter can almost be thought of as mass instant messenger, and the only people who have to see what you write are the ones who care. What's also nice is that I can follow some of my geek idols, like Wil Wheaton, M.C. Frontalot, Lore Sjoberg, and Jonathan Coulton, and see who they're following. Which is cool.
Perhaps I'll log into my twitter account and tweet only the word "Poopie"... It would sure as heck be more interesting than some of the tweets I see.