To me it's just another form of RSS (which I don't personally think is dead at all). The tweets I like are the links to interesting web pages. It's like a shared bookmarks if you will.
What I don't like are the cryptic messages or the plain boring ones ("I'm at the airport" -- who cares!). Although I'm guilty of posting irrelevant twats too, but like to think mine are at least of slight interest/amusement.