I never got why people liked Twitter, but I saw enough people I respect using it (like Ward Cunningham, Dave Thomas, Venkat, and Neal Ford, to name a few) that I decided to try it out... I like it. A lot.
Now that I can "twit" from my iPhone, I don't have to use desktop time to update or track other people's streams. I can post or read at a stop light or in an airport.
Also, the iPhone has a killer app called Twinkle that shows me Twitter feeds based on my location. There's something compelling to me about being able to see feeds within 1-2-5-10-100 miles from my current location. And it's amazing how many people there are "Twitting" on Twinkle within 2 miles of my house.
(In order to use Twinkle, you'll need to "jailbreak" your iPhone. You'll find a nice GUI on the ZiPhone page. It's a busy page, you'll have to navigate a bit. Also, only jailbreak. Don't unlock or activate unless you really know what that means.)
And just now I read an article titled Tweeting for Companies 101. Don't let the title fool you... while there's a decent amount of information for a corporate Twitter movement, there's tons of good information for the individual user as well.
Here's a page of Twitter Apps to get you started. Scroll down to find non-Windows apps.
Here's my link. Come visit. Get addicted too. :)