In my opinion, a person shouldn't become self-employed unless demand for his or her services is high and the competition is low. I've seen good people suffer economically because they wanted to stop working for other people and set up their own shops. Once a former employer becomes a competitor, some self-employed people find themselves at a real disadvantage.
I would say that the most successful self-employed people have found a popular niche market for their goods or services, and don't have to worry about being undersold by a larger company. A self-employed baker who makes customized cupcakes offers something a commercial bakery across town cannot. A self-employed tax preparer, on the other hand, must compete with well-known tax preparation companies with much larger advertising budgets and staffing.