Okay, there are a lot of interesting responses on this thread, and I am willing to admit that I understated the particular value of a major.
A couple of points:
1) I was not referring to an engineering major. Those who go through an engineering program do indeed learn a lot of specific skills that they can immediately apply. Of course, this specialization, like all specializations, comes at a cost of a more general education.
2) Yes, a major is important. More important than the particular major (I would argue) is the entire course of study that a student undertakes. Major courses and non-major courses should narrate the particular set of skills. Undergraduates should work on thinking about how their entire course of study prepares them to enter the working world. It is my belief that motivated and excellent students can connect almost any major course of study to almost any future career--even philosophy and women's studies majors.
3) To the Chem major who talked about how chem students get paid to study at the graduate level. So do philosophy majors. I know this from experience.
4) My advice to any undergraduates reading this thread is to consider carefully how and whether a particular major aligns with your interests and strengths as a student and as a person. It is a competitive market. For this very reason, it is essential that students take subjects that they are interested in and good at. This interest will come through in interviews, in performance, and it will reflect your strengths.
5) All that said, the purpose of a bachelor's degree is to introduce you to two aspects of your education. An education should be both general and specific. There is not enough time in 4 years to gain enough specific knowledge to be of much use as a specialist. There is enough time, however, to be introduced to the specific nature of a field and to determine whether and how you would like to go further in it. The primary effect of an undergraduate education, in my view, is to give you general knowledge and the general skills I mentioned in previous posts. The introduction to a specific field, to my mind, falls under the general category--as an introduction to the idea that particular fields of inquiry have particular methods and criteria of knowledge.
6) Enough! or Too Much!