I started my business unexpectedly in 1994 when I found myself out of a job with $70K in debt. While it took me 90 days to land my first client, I picked up a job supervising a catering kitchen, and also went to teach evening education classes at three local universities in Atlanta. It is often better to have a deadline or be forced or you won't make the jump. It takes everyone a different amount of time. I was debt free and earning six figures in 18 months.
The $100 Startup Book by Chris Guillebeau is a great book that details many side projects / hobbies that turn into highly successful companies. http://100startup.com/
"These are the Things" is an example from the book. There story is detailed here:(http://thesearethings.com/about/). They built their business over 9 months before they quit their day jobs.
Here are additional examples from one of my favorite authors/Blogger Tim Ferriss.
Personally I just left my director role at Best Buy to start my own company. I had been doing small business consulting on the side for the last 6 months and decided it was time to take the plunge. There is no average time on when founders decide to switch full time. I have seen it be as little as a week to up to many years. It all depends on how quickly it is able to support your lifestyle that you have chosen. My decision was due in large part to a personal desire to work for myself vs. a large corporation and have the ability to build something from nothing.