There was an interesting article earlier this week in the Wall Street Journal, on mental health concerns in college students. It's no secret that mental illness often has an onset in the late teens and early twenties. It's also not a surprise that there are significant stressors associated with college (or graduate school), including being in a new environment w/ a different (possibly much smaller) social support structure, the pressure to succeed academically, the need to budget time much more self-sufficiently than at previous stages of life, and simple things like lack of sleep. As a result, sometimes as a faculty member you come across students who have real problems.
In undergrads, often these issues manifest as persistent erratic or academically self-destructive behavior (failure to hand in assignments, failure to show up for exams). Different faculty members have various ways to deal with this. One approach is to be hands-off - from the privacy and social boundaries perspective, it's challenging to inquire about these behaviors (is a student just having a tough time in college or in a particular class, or is a student afflicted with a debilitating mental health issue, or are is the student somewhere on the continuum in between). The sink-or-swim attitude doesn't really sit well with me, but it's always a challenge to figure out the best way to handle this stuff.
In grad students, these issues can become even more critical - students are older, expectations of self-sufficiency are much higher, and the interactions between faculty and students are somewhere between teacher/student, boss/employee, and collaborator/collaborator. The most important thing, of course, is to ensure that at the end of the day the student is healthy, regardless of degree progress. If the right answer is that a student should take time off or drop out of a program for treatment or convalescence, then that's what has to happen. Of course, it's never that simple, for the student, for the advisor, for the university.
Anyway, I suggest reading the WSJ article if you have access. It's quite thought-provoking.