I've found twitter is awesome for finding out whats going on during big events. I was at a gaming convention and I was using to find out when there were cool demos, where stuff was being given out, etc.
Other than that I don't have much of a use for it.
What's interesting to me though is that Twitter is an amazing tool to propagate news at an unprecedented speed. People tend to tweet on an impluse, i.e. as soon as something happens. The news that Osama Bin Laden has been killed broke on Twitter an hour before the official announcement was made. During the London riots people used Twitter to warn other of danger and to organize clean ups. Twitter is the perfect example of how technology now allows us to share information immediately and globally.