In my opinion (and this certainly is in agreement with the practice in my department and university), the advisor's primary job is to supervise a student's work on an MS Thesis or PhD Dissertation. At our institution, advisors are also responsible for making sure that students satisfy the specific course requirements for their degree.
I make it a point to discuss expectations with any student who asks me to be his/her advisor. If the student has unreasonable expectations of me, I'll simply decline to advise that student. If the student isn't willing to meet my expectations, then I'll also decline to advise that student. Sometimes students decide after this conversation that they don't want me for an advisor. The important point here is that both parties should understand how things will work before the student starts working with an advisor.
My expectations of students include:
I meet with my advisees regularly, most often once a week. Each time that we meet I try to lay out specific work for the student to attempt during the next week. I expect students to regularly achieve these short term goals- if a student is consistently unable to do so, I may terminate the advising relationship.
I expect students to write and edit their own manuscripts. I am not happy if the drafts I'm given are filled with typos, spelling errors, or grammatical errors. I want to spend our time together discussing mathematics at a higher level rather than copy editing text.
I expect students to produce research of publishable quality. We plan out papers in advance, including who will be first author (usually I expect the student to take the lead in writing the paper and that they will be first author.) I expect that papers will be submitted before a student defends his thesis or dissertation.
In return, I think that students can reasonably have some expectations of me:
I will be available to meet with them on a regular basis to discuss their project.
I will carefully review their drafts and provide substantive written comments.
I will be willing to write recommendation letters on their behalf.
I don't believe that the general "professional development" of graduate students is the particular responsibility of advisors. Rather, I encourage my advisees to take advantage of
available opportunities such as attending workshops and conferences, professional development programs offered through out graduate office, and our institution's writing center and disseration bootcamp.
My advice to any graduate student who is in the process of selecting an advisor is simple- discuss your expectations with the professor before filling out the paperwork to make him/her your advisor.