I've had a Twitter account for 1-2 years. I'm still not sure what Twitter is good for. FB is better for social networking with one's friends. I've started using Google+, which is good for pursuing hobbies. I've discovered lots of interesting memes and artwork through Pinterest and tumblr.
On Twitter, I follow a few dozen celebrities and scientists, who rarely post anything I find interesting, as well as a handful of magazines and organizations. Occasionally I discover an interesting Website and I bookmark it.
I use Twitter about 5 minutes a week.
The best thing that happened to me on Twitter is this: I "tweeted" to Alexis Wineman (recent Miss America contestant with mild autism) and she tweeted back. It was one of the few brushes with celebrity I've had in my life.
If you're on the fence, I recommend not bothering with Twitter.
_________________
DRzero