When Twitter was launched it received a lot of bad press due to its apparent futility.
As more and more people are subscribing to this social site, and people have had more time to experiment, they are questioning their initial thoughts.
One example is Clive Thompson. In an article he wrote for Wired Magazine, he stands up for Twitter.
He suggests that Twitter is not good for the random sequence of messages one gets every day from our friends but rather for the collective of messages one gets from each one of our friends.
"Twitter and other constant-contact media create social proprioception [(your body's ability to know where your limbs are )]. They give a group of people a sense of itself, making possible weird, fascinating feats of coordination."
He goes on to say that even if Twitter happens to be replaced by a new tool providing similar functionality, the "bug" of twittering is here to stay and will influence social tools to come.
A similar opinion is shared by Stephen Wellman who sees Twitter-like applications as the future of presencing tools and also as a useful business tool.
I feel I cannot really comment from personal experience, not having signed into Twitter yet myself. However, I can see how and why people's perceptions are changing and I can see the potential for quick, intra-organisational communication. Celebrating success, telling about new projects, sharing highlights of important what-not-to-dos, sharing stories, can all be enhanced by Twitter (or similar applications like Pownce, for example).
Additionally, because I am very aware of the importance of trust and a sense of belonging in social networks (personal or professional), I can understand Thompson's point of view. Knowing someone's little steps, random thoughts, burning questions, helps one build a sense of that person, helps getting to know him/her. And that is the core of any successful trust relationship.
And just to put all these theories to the test, I will be signing in to Twitter... now!

Twitter ... bad press? Not the press I read, for sure. Riccardo wrote this earlier today about Twittering from within Second Life: http://chaosncoffee.com/blog/2007/07/18/down-into-the-xverse/.
I am signed up but have managed to avoid getting too deep into it, plus I prefer Facebook as my status message of choice.
But I think beyond geeks, the Twitter model (if not the product necessarily) will find a home in business and projects for the reasons you mention above. Jaiku already has channels, but I expect Twitter groups will come soon.