I think i have little to contribute to your question on mentoring, this is because i recently picked interest in the subject and did some literature search on the subject and found very useful insight into the subject.
My understanding of 'students' in your question implies both undergraduate and postgraduate students.
Just as you rightly said mentoring of students is done in various ways, formal or informal. Recent scholarship show that mentoring influences the learning process positively resulting in enhanced students performance, increased retention rates reduced attrition among students etc. This is possible because the mentoring relationship (mentor-mentee) goes beyond the conventional student-teacher relationship and the mentee learns from the experience of the mentor.
Different individuals and institutions have different approaches to mentoring. Yes there is a standard for mentoring especially in institutions where formal mentoring programs are institutionalized, however, these standards could be institution, specialty or country specific (i stand to be corrected please) but that is my opinion. A good example of a formal mentoring program i have come across in literature is that of University of California San Francisco. Another standard mentoring program i have come across from Africa is the mentoring program in the health sciences from one of the universities in Uganda, i have come across their mentors manual in the health sciences. The Medical Education Partnership Initiative in Nigeria (MEPIN) is also working along that line through collaborative efforts in developing and strengthening a standard mentoring program.
It is also interesting that we can benefit from E-mentoring i find that useful as well, though it also has its own draw backs.
Despite the numerous benefits attached to mentoring, there are certain negative draw backs as well, such as unwillingness of the mentor to let go of the mentee when it is time, mentee may leave halfway, godfatherism among others.
You may find this presentation from our local conference from one of our professors useful.
At my university in Sydney Australia, peer mentoring or PASS (Peer Assisted Study Sessions) follows the Supplemental Instruction (SI) model, in which first year students are mentored by senior students from the same discipline. These sessions as ePASS are also delivered online. You can find out more about this program at http://www.uws.edu.au/pass
Mentoring here means group work facilitated by the mentor; students studying together, solving problems, and working out answers, and not being given answers.
These sessions help not only students who are struggling to pass but also high achievers as students feel more positive about their learning while working in a collaborative, discipline-specific context.
University study can be a very lonely experience for those who fail to make friends or belong to a group. Peer mentoring sessions can provide these students with an increased sense of collegiality with their peers whether they are mentoring or are being mentored.
There are no known side effects of mentoring, provided it remains facilitation of learning and does not end up becoming a tutoring activity, which can then create problems such as dependency as well as contradictions between what academics are expecting students to achieve and what the mentors might think is the best and the quickest way to “teach”.
A two day training is offered to mentors where skills of facilitation, so integral to the philosophy of peer mentoring, are developed. There is also a manual which has been specially developed for mentors.
Satisfactory timetabling to suit both mentees and mentors can however be a challenge, and mentees’ ongoing attendance at these sessions is also not guaranteed as there is no mandatory requirement to attend these voluntary sessions.
Here are some articles about PASS and PASSwrite (emphasising academic writing development) from those involved in PASS at my university.
Williamson, F., & Goldsmith, R. (2013). "PASSwrite: Recalibrating student academic literacies development." Journal of University Teaching & Learning Practice 10.2 (2013): 5- Available at: http://ro.uow.edu.au/jutlp/vol10/iss2/5
Power, C., & Dunphy, K. (2010). Peer facilitated learning in Mathematics for Engineering: A case study from an Australian University. Engineering Education, 5 (1) (2010), pp. 75–84. Available at: http://www.sciencedirect.com/science/article/pii/S1877042812040967
Dearlove, J., Farrell, H., Handa, N. & Pastore, C. (2007) Evolution of peer mentoring at UWS. JANZSSA - Journal of the Australian and new Zealand Student Services Association. Editor - Jim Elliott. Number 29, 2007. (pp. 21 – 35)