Just one of things that is interesting about Twitter is how many services have been built upon its simple interface to provide additional features. For a service that has yet to hit mainstream, it's germinated a whole eco-system of apps.
Here's some of the Twitter tools I like best.
I don't bother with desktop apps or Firefox plugins, but these I find useful.
TwitterLocal, see what folks around the Hood are saying.
TweetScan, search keywords. Or search you user name and see what others have said about you that you might have missed.
TweetStats, all kinds of stats about your Twitter use. I Tweet most often on Saturdays and at 8 a.m. and 9 p.m. I talk to @Newscoma a lot.
Summize, another great Twitter searching tool.
Twitterholic, if you need Twitter "friends" to follow.
Twist, Compare keywords. Here's "big brown and belles."
TwitterFeed, great RSS to Twitter app.
Who Should I follow?, an interesting one to find new friends on Twitter.
Do you have "must haves?"
Here some more best of Twitter tools blog posts:
CyTRAP Labs' choice - free tools - 12 best Twitter tools
40+ Twitter Tools for Extended Twitter Experience from To the PC
The Clever Sheep: How Many Twitter Tools Are There?
Charles Arthur: Your suggestions please for the 20 best Twitter tools
Oh, yeah, follow me here.