I've been reading a slew of interesting -- and often depressing -- links from academia from the end of 2010. Flavia's entry on students sharing more about their "lives than I have any desire to know" made me think of my own struggles with this issue. I generally want to respect the privacy and autonomy of students. For example, students have a specific number of absences that are "freebies" so they need not explain or justify any absence to me. However, if they do need to speak to me, I tell them to speak to me sooner, rather than later, about a proposed solution, rather than gory details of the problem.
While I am quite sympathetic to well-timed and reasonable proposals, otherwise, and especially when it comes to grading, I typically respond along these lines:
I would never presume that "school should come first" relative to the other events in people's lives, but nonetheless my obligation is to assess what happens in the classroom. Honestly, it is impossible to play Solomon and judge the often difficult circumstances of people's lives, or to try to figure out how things might have been absent those challenges. So, I pretty much stick to the grading criteria in the syllabus.