It's really no different than any other information medium. Do you watch TV? 90% of that is dribble.
What I like about Twitter is that it's much like a newspaper. The Tweets are 140 characters and a lot like headlines. If the Tweet is interesting, I click on the link and dive into the article. The misconception that non-Twitter users hold is that the 140 character Tweet is all there is. That's not the case - the Tweets lead to more detailed web pages, photos, etc.
If there's news or info that I'm interested in, it comes to me. I don't have to go chasing it. A lot like RSS feeds but a hell of lot easier to find the stuff that's relevant.
Let's say you're in the technology business. It's your job to stay current. So I follow nyt_tech, silicon valley insider and various Mac and Apple tweeters. For entertainment, I follow a few comedians. For sports, I follow ESPN, TSN, Chad Ochocinco, Will Carling (rugby). I follow guys who's opinions I respect (industry and otherwise).
MUD, if you're truly interested and not just a naysayer, try it for a month. Download a client like TweetDeck, follow people from your industry, your hobbies, etc.
Honestly, everyone I know who thumbs their noses at Twitter has never really tried it.