The only use I've seen for Twitter is the ability to follow companies for status updates or important announcements. The local university here is looking to do this for students, and I've seen several online services use it for downtime/updates.
But an RSS feed does the same thing already, and is in a format that doesn't make me have to subscribe to yet another site. With feedburner, there's no worry about feed traffic getting out of hand either. So I don't really see the point, except maybe as a marketing tool to the Twitter crowd...
Then again, my startup uses it too (in addition to our blog/RSS), and my business partner really likes it. So maybe I'm just clueless :)