Being the right kind of demanding as a college instructor As part of my work as a graduate student in maths I currently teach a basic second semester calculus course. It seems like every semester I teach, one or two students want some sort of special privilege to turn in homework late for a month or take a test a week after they are supposed to. Many times they have somewhat legitimate reasons (documented depression, getting a divorce, wife having surgery.....). How should I handle these cases? I am not big into putting up with lots of late homework or late tests, but then again I would want someone to be lenient with me if things such as the parenthetical reasons above arose in my life. 

How should I handle students with such situations? Should I write them off and just feed them to the dogs or should I allow them to catch up at their own pace? My honest opinion is that school is a sort of competitive game (Bad, yes, I know) and if they lose they lose. We do not shorten the football pitch because some club's striker is not a good runner. However, I think students should be allowed to have a chance to make things right.
If people have a legitimate reason for wanting an extension of the deadline, I would simply give them the extension. If they cannot provide a good reason, i.e. they simply procrastinated too much, they have to take responsibility for their behavior, and they do not get the extension. 

This has nothing to do with being a hard-ass, but being fair. Other people have done the work, and giving people that procrastinated an extension is not fair to them. In addition, getting work done that you where assigned (even if it is hard or boring) is a valuable lesson to teach a student. Their future boss will also not be sensitive to a missed deadline because of procrastination.