So i worked at Odeo and was involved in the initial product exploration and creation of Twitter.
It was not created accidentally. We were experimenting with and thinking about the way people communicate. What if it were casual and open. In the same time as we did the first prototype of twitter, we also built hellodeo, very similar to stickem/dailyboot, a kind of social voicemail, a mocked out groupware 2.0, etc...
We looked a lot at SMS, interviewed teens who used lots of sms, played with txtmob.org and UPOC as examples of something similar with explicit groups. At one point i remember, Ev i think, saying "what if we just made a clone of UPOC, but without explicit groups." Or something to that effect.
We started using it, and with a couple hundred users who liked it, we were sending hundreds of thousands of tweets a month. Few people used the first versions, but those who did, became hugely addictive. The half a dozen other prototypes we built, didn't have passion. Twitter, people loved or hated, or both.
Evan Williams then took his resources from selling Blogger.com to google pre-ipo, and was able to buy the VC's out. His original idea was to do Obvious Corp, continue the prototyping and process which had created twitter. Unfortunately Twitter overwhelmed Obvious, and they spent the next couple of years just playing catchup.
It's not hard to do good new product work. Spend time really getting to know a space, look at practices people are engaging in. Then start thinking about variations. Are people doing something in their social practices, by using technology NOT how it was intended. What if you shaped tech for those intentions.
Twitter's lesson is you can do prototypes until you find something which is compelling, then keep doing what people want, based on their actions (not what they say they want.) If you do that, then you'll eventually figure out a business model.