I resisted Twitter for a long time. The tweets I read were boring, I didn't see the point of making one-sentence updates on what I was doing at whatever moment. I kept hearing that it was impossible to explain its appeal, you just had to try it. So a few weeks ago I did, and yeah, I think I get it now. LJ lends itself to one sort of conversation, IM to another... Twitter is somewhere in between, with a bit of chat room thrown in.
Another metaphor posted by a Twitterfriend: "MySpace is the dance club you used to think about trying. Facebook = summer camp reunion. Twitter = your favorite diner/bar/cafe."
People use Twitter in a million different ways. The "here's what I'm doing at any given moment" stuff is pretty boring, yes, but relatively rare among the people I follow. I'll post things that I want to remember later, things that would be an LJ post if I ever had time to develop it into an actual essay, fun links, and in the recent snowstorms we've had I've found it useful as for "I'm going out, release the hounds if I'm not back in 2 hours" and "home safe" messages that would just clutter up LJ.
I do think it's pretty counterproductive to crosspost them to LJ. The real-time-ness of Twitter is a large part of what makes it interesting, and it gets tiring reading one half of conversations (in the actual Twitter interface, you only see messages between people if you are following both of them, so you get the whole conversation).
I like it. But to each their own.