Read this paper and others like it with an eye towards discovering which aspects of the graduate experience your students may be having trouble with, or may not realize the importance of. Try to see the experience from their perspective, which will be different for each student, because each student has a different background and different talents and goals.
The roles of an advisor include:
To improve the atmosphere of your interactions:
In the short term, a good advisor will work with students to set priorities and to find a balance between doing research, reading, writing, satisfying TA and RA duties, publishing, and coursework. Although advisors may not be able to give advice on all administrative aspects of graduate school, they should at least know the appropriate people to refer students to for assistance with degree requirements, funding, and so on.
When you meet with your students, pay attention to them. Try to help them to identify their interests, concerns, and goals, not just how can they meet what *you* see as good interests, concerns, and goals. Know what they're working on, and what you discussed last time. Take notes during meetings and review them if you have to.
Give them productive feedback, not just a noncommittal "ok, sure" or a destructive "why on earth do you want to do that?" Remember that your students are still learning. If you tell them that a problem they're interested in has already been explored by Professor X, make sure you follow up with a reference that they have access to, and a discussion as to whether the problem remains a worthwhile area to work on, or whether there are new open issues raised by Professor X's work, at the next meeting.
When reviewing a student's paper or proposal, write comments on the paper itself: verbal comments aren't as useful. Give the feedback promptly, or it won't be much help. See the section on feedback for suggestions about giving useful comments. Don't just wait until they hand you something to read: insist on written drafts of proposals, papers, etc. Help them develop their rough ideas into publishable papers. Give them specific, concrete suggestions for what to do next, especially if they seem to be floundering or making little progress.
Advisor-student relationships can break down if the advisor is setting goals that are too high or too low, or if the advisor is exploiting the student to meet the advisor's needs, not the student's. In my opinion, it is never appropriate to develop an intimate relationship with one of your own students. If this should happen, you should not continue to advise them (whether the relationship continues or not).
Encourage your students to choose a topic that you're *both* interested in and that you're knowledgeable about (or very interested in learning more about). Make sure that they have the appropriate background to understand the problem, and that the methodology and solution they identify are appropriate and realistic. Give them pointers to useful references and help them find them (this can be a mysterious, difficult process for graduate students). Make sure they're aware of other researchers and labs who are doing similar work, and if possible, arrange for them to visit these labs or meet the researchers at seminars or conferences.
Women faculty often feel obligated to mentor every woman student in the department, attend every committee meeting, and get involved in every debate, whether they want to or not. While you can't solve all of the problems in the world, you can at least make a difference by giving other women (and men, for that matter) the sense that you do care, and that you think women's issues are important, even if you don't have time (or the inclination) to get involved with every problem.
The relationships you develop with your students will vary. With some, the relationship will be purely professional; with others, you may become closer friends. As an advisor, it is your responsibility to ensure that your position of authority over the student is never abused. As mentioned previously, graduate students should not be used as a means to a promotion or a better publication record. These will be side effects of good work in conjunction with your students, but should not be the goal of your relationship.
Because you are in a position of authority over your students, you must make sure that you both know where the boundaries are. For example, getting a student to help you move some furniture is usually quite easy if you're doing a good job as an advisor, since they feel indebted to you for your advice and support. This isn't a problem in and of itself. However, using explicit or implicit threats to force the student to help you out is a severe violation of professional ethics. Your students are also your colleagues, and should be treated as such. A good question to ask yourself before asking a student for a favor is whether you would feel comfortable asking the head of your department for the same favor. If the answer to this question is "no," then you may be exploiting your position and abusing your relationship, and you should seriously reconsider your motivations and behavior.
In my opinion, it is never appropriate to develop an intimate relationship with one of your own students. If this should happen, you should not continue to advise them (whether the relationship continues or not). Not only would this be a clear case of sexual harassment, but your judgment about the student's professional life cannot be objectively separated from personal feelings in a close relationship.
Dating students (or even asking them out where the implication of a romantic relationship may exist) is a bad idea, even if the student is not one of your advisees. They are bound to feel intimidated and uncomfortable, and at many universities this violates the sexual harassment policy.
Read your university's policy on harassment, and err on the side of conservatism when in doubt, for your sake and the student's. Next to Becoming Part of the Research Community.