It's a question that brings up all sorts of issues: issues of professionalism, of respect, of our ability to promote ourselves in our field... etc., etc., etc. But I think one poster made a very astute comment:
I think that some people automatically assume that working in a library makes them a librarian. I also think that some people think having a fancy piece of paper makes them one too. I really think that being a librarian is something above and beyond both of those things. When I was in law school, a professor always used to tell us that graduating from law school doesn't make you a lawyer. It just means you have a degree in law. I feel the same way about librarians. I know some librarians with MLS degrees that I don't think have any right to call themselves librarians. On the other hand, I know a lady who has no MLS, but is the most amazing librarian I have ever met, and I would not be upset if she called herself a librarian (which she won't).I think this comment cuts right to the heart of the matter. People dither about what a degree means, when really the degree shouldn't be an end in itself but a means to an end. I'm certain that ML(I)S programs are turning out some graduates who aren't really going to be good library professionals. (There are even one or two people in my own program about whom I often wonder why, precisely, they're putting themselves through all this (and other SI folk who read this blog, let's keep speculation of/discussion about precisely who and why out of the comments here, because it's not really the point of this post. ;) ) ) The point of the program is not (or should not be) just for you to get the fancy piece of paper. The point of the program, as it should be with all education, is to give you skills and knowledge, to make you a more effective and learned person, in hopes that doing so will change how you live your life/perform your job/etc.
The degree doesn't make you a librarian. The ability to perform the work intelligently, conscientiously, and effectively does. The degree is supposed to help you do that, but it is not always necessary or sufficient. It's (sadly) very easy to get through two years of school and not really pick up anything useful. It's also possible for someone who is sufficiently driven and self-guided to pick up everything s/he needs to know without going to school.
Of course, that's my own perspective, which is probably biased by my humanistic educational background. And in reality, when making employment decisions, degree holders should generally get preference over non-degree holders -- simply because you are more likely to have the skills, knowledge, and ability to think necessary to be a good librarian if you have been given one to two years to learn, to practice, and to consider the important issues of the field. But I do believe that many people who work in libraries are not really librarians, no matter what their job title says.
The next question, of course, is: What makes a librarian, if it isn't the degree? That is perhaps one to take up next time... or in the comments. I'd be very interested in hearing what other people think about all this.