Obviously, it depends on what you are going to do after you quit your day job. If you are not going to work for the rest of your life then it is a no-brainer that you need to have lot of money saved !!!
If you are going to work part-time or going to start a business/consultancy and are not sure of your initial earnings then it depends on your risk taking ability to have a "safety net" of your earnings. It varies based on the various factors - your expected earnings, expected period, your type of business, your age, your family size etc.
A good thumb rule would be to have a "safety net" earnings anywhere in the region of three months to two years. This can ensure your that you can focus on what you have planned to do.
Best of Luck !