What are people's views on this?  To be specific: suppose a PhD student has produced a piece of original mathematical research. Suppose that student's supervisor suggested the problem, and gave a few helpful comments, but otherwise did not contribute to the work.  Should that supervisor still be named as a co-author, or would an acknowledgment suffice?

I am interested in two aspects of this. Firstly the moral/etiquette aspect: do you consider it bad form for a student not to name their supervisor?  Or does it depend on that supervisor's input?  And secondly, the practical, career-advancing aspect: which is better, for a student to have a well-known name on his or her paper (and hence more chance of it being noticed/published), or to have a sole-authored piece of work under their belt to hopefully increase their chances of being offered a good post-doc position?

[To clarify: original question asked by MrB ]

In my opinion, as a rule the supervisor should not be a co-author in the main paper taken from a student's thesis, even if he has contributed substantially to it, and even more so in the circumstances you suggest. The student needs to publish much more than the advisor does.
If the advisor him/herself is a junior person and has given a lot of help and a very good idea to the student, then I suppose that an exception might be reasonable. Also, a thesis project might spawn more than one paper, of course, in which case it's fine if the advisor is a co-author in some of them (always assuming that he has done much more than suggesting the initial idea).
Of course, it may happen that the student is weak, is given a good project, and needs to be guided step by step, so that at the end the advisor has contributed much more to the thesis than the student. Then a joint publication is in order. Such a student will most likely not pursue an academic career, so it does not really matter.
[Edit] Let me try to clarify my thought, and perhaps be less radical. What I am going to say applies to pure mathematics; I am very much aware that in other fields things may be completely different.
A good thesis project is one that is both interesting and feasible. Devising such a project in pure mathematics is hard; most beginning students, even very bright one, need guidance, particularly in countries, like Italy, where the PhD program is 3 years. A student has a lot to learn before getting to a level to understand and appreciate a research project; it is clear that a student in a short program does not have a lot a time for trying and failing (which is, of course, very educational, but also time-consuming). Now, some students come up with their own problems and solve them, but in my experience they are exceptions.
I consider it part of my job as an advisor to suggest a problem, or an area of investigation that can be profitably mined from the student. After that, I follow the student, teaching her (let's say she's a woman, purely to avoid the "him or her") whatever I can, trying to dissuade to pursue lines of work that seem barren, uninteresting or risky to me, and also giving ideas. Sometimes she will get stuck; and then I'll think about the problem, to see if there is a difficulty that seems unsurmountable, or if there is an approach that she can try. After some time of this, if she is good she will take off on her own, and understand the problem better than I do; then I will consider that I have done my job. When she writes the paper, I will not be a co-author, even if I have obviously contributed a lot to the project.
Of course, different students require very different levels of involvement; but in my experience, it is not necessary true that the best student are the ones needing less help. Also, a lot depends on the problem.
Now, some people tend to give students substantial parts of their research agenda; in this case the advisor is directly interested in making progress, gets more involved, and is more likely to be a co-author. This is another case in which joint authorship is perfectly reasonable. I would not want to conclude anything about a student from the fact that have published the main paper from their thesis with their advisor.
