The real power of Twitter, it seems, is not that it lets us tell everyone when we're going to pick up the groceries or what happens to be on our minds at some random moment, but rather that it's an application that easily, and mobile-ly, hooks up to everything else. Many of the Twitter applications touted as top ones are mashups that either let us Twitter ourselves with useful info -- say inform our Calendar or iGoogle page of something we dont want to forget -- or have us sent things we want on the go, such as BBC headlines. I suppose the application possibilities are the reason they just got money from Union Square Ventures, even if Union Square says they don't see what the business model is, yet.
One other possibility I see when we get fancier about mapping and remapping and re-configuring data, in multiple dimensions and with overlays and semantic parsing: We'll see not just the most popular "twits" but also get a real cloud-formed look at what our zeitgeist is, where our consciousness is going that may be richer than any Yahoo "buzz index". (It's kind of a 21st-Century Megatrends that's a more real read of society than indexing newspaper headlines can ever be, because it indexes real-time data from lots and lots of people -- even if the sample is skewed toward whatever demographic or type would use the technology and share on it.)
This is all predicated, of course, on the assumption that those trying to Twitter with automated twits, and so on, will not end up killing the system by overloading it with spam.