I don't twitter, but I know people who do.
The concept appeals to the narcissist in me. It amuses me to think that friends etc could know what I am doing at any given time (in 140 characters or less). I know that if I started doing it, I would update frequently and it would be interesting to me and maybe whoever is completely obsessed with me to the point that he (I would hope it's a he, because, well... just because) has an alter set up in his basement. He would, of course, add a screen of my twitter updates so he could sit there watching it and know what I am doing at any given moment.
I am totally creeped out by my own imagination.
I would also be very tempted to take my twitters (is that what you call them) and use them to write my own Ulysses. Mine wouldn't be called Ulysses though. And I would not stuff it full of symbolism. I would try to make it sort of humorous too. And I will have no sentences that go on for more than 2 or 3 pages. God, I dislike James Joyce.
I haven't read Ulysses, but I know people who have.