While I have a culinary degree, I agree with Lagom and Lauren, they are not absolutely necessary, and as Lagom pointed out, they can be very expensive, especially if you want to go to one of the really good schools. It really sucks when you get out of culinary school, with a mountain of debt, and get stuck working $9-10 per hour jobs. And yes, you will still be stuck working those types of jobs for awhile, until you build up some experience. I have known many a chef that never went to school and they excell in what they do. That being said, I do think that a culinary education can kind of fast track a career. Yes, you still have to "pay your dues" and build up experience, but what I think culinary school does well, is that it exposes you to a lot of different cuisines and a lot of different chefs, each with their own way of doing things. The amount, and variety, of things that you are exposed to at culinary school would take you years and years out in the real world..
In other words, there are pros and cons to each path, but each path can get you where you want to be. It mostly depends on whether you are willing to work for it or not