Signed up to Twitter experimentally, and have been using it off and on.
Twitter for me is one of those things that needed to slot into the way I do things anyway. I reckon a lot of holdouts on new hotnesses like Twitter and Facebook (like me) have to wait until an external factor pushes them into it (this is usually boredom). For me, this was a critical mass of people I know using it, and it offering something new.
The "Something New" for twitter was the lightweightness of it, and increasingly how ubiquitous it is. It's a really simple idea, and yet is made special by the like of Neil Gaiman, Stephen Fry, and Graham Linehan updating many, many times a day about what they're up to. You can even ask them stuff, and they may even answer. It's a pretty sobering thing to think that in my short time on this earth, we've gone from reading bibliographies and forewords about people, to finding out where they're going for lunch. It may seem petty and gimmicky, but I think it's shit cool.
Another interesting phenomenon is how news seems to break in Twitter before anywhere else, and sometimes precipitates the olde-world press picking up the story. This is freaking great, because it means that news that people actually care about will get picked up, and news outlets that don't pick up stories that are on the very nerve endings of people everywhere. Such as the Revolution in Moldova. Information like this is key to existing as a human, and it's decentralising news. Sure, there's news that you want to seek out and read, but the trends in twitter give a pretty good read on what people are actually thinking and talking about. This is extremely powerful. It's pretty skewed right now due to the demographic of the average Twit, but imagine if more and more people started doing it? It's data that's extremely powerful, because it's something that you can archive, store and analyse later. I'll bet the corpus of tweets from this decade will be extrmely interesting in 100 years.
Of course, like any web service, there's also an awful lot of nonsense. There are also a metric assload of bots (not all of them stupid, Maria pointed us at some piece of equipment they have hooked up to Twitter recently) I'll bet having tweets from stuff like this (i.e. the non-stupid bots) will be also interesting as part of the giant timeseries we're producing.
Anyway, my own personal thingo is at where you probably imagine it to be. I've been using twirrsi (a plugin for the IRC client I have open in a screen session anyway) and tweetie on the iPhone.