Twitter can be endless streams of people telling us they just brushed their teeth. And in those (majority) instances, it’s worthless.
However, it is a good informational tool. I’d suggest following MichaelHyatt and jowyang. Michael is the CEO of Thomas Nelson, and he treats twitter with care. Jeremiah Owyang is a research guy for Forrester, and his feed has a lot of useful information, often dealing with trends.
It also can be used as a good marketing tool. You can “push” messages to your followers. Those messages are ephemeral — only appearing once — but they should be fast and easy to produce. You never know what may result. A word of caution there, though — if a user’s outgoing messages are all push, they will soon be ignored. There needs to be a healthy mix of featuring others’ sites or information and a bit of personality.
If you have a significant list of followers (which I do not), Twitter can be used as a free instant polling mechanism.
Twitter search is a great tool for finding way more up-to-date results for almost anything, compared to what Google can yield.
Finally, you do not have to follow those who follow you. Further, if you are following someone who writes endless drivel, you can just un-follow and be done with that.
I’d suggest you claim your name right away, as it may not be available tomorrow. I see Twitter as a growing phenomena — at least in the short term.