This mimics my experience almost exactly. I 'forcefed' it to myself for a couple of weeks, almost agonizingly, and then discovered that it could actually be somewhat useful.

Couple of specific examples:

- a few weeks ago some major storms came through Cincinnati. 1.5 million people lost power and there was major damage everywhere. With power and Internet being down for several days, communication was very difficult. I follow several Twitter-ers within the Cincinnati area that provided updates to power restoration and storm cleanup news via their smartphones, which I read on my phone. This was very helpful

- I get CNN breaking news alerts via Twitter. To me this is a less obtrusive way of receiving breaking news than via email or rss feed (email and rss feeds both have a way of piling up)

- I follow a few CEO's that use Twitter and I find it rather interesting to see how they spend their time, and there have been a few instances where I've actually improved some of my own habits / workflows based on ideas from following these CEO's Twitter feeds

- Friends and family spread throughout the country. Hey, it's interesting knowing what people I care about are up to. The mundane things that they Twitter are typically items that wouldn't come up in everyday conversation. By Twittering we get a window into each others lives that sparks real-world conversation later. "Hey, I saw on Twitter that you went golfing the other day. Where'd you go? How'd you do?"

- Just this morning one of my friends Twittered about SpeedFiler for Outlook. I gave it a try and absolutely love it. Never would have known about it otherwise.

- Me and my co-workers travel a lot and use Twitter to announce location updates. "At MSP for 3 hour layover, anyone else here?" can be a useful tweet

YMMV