I like this policy because it puts the burden of time management on the student. If a student finds herself in the position of asking for an extension repeatedly, this is good evidence for both of us that she is having problems with time management. On the other hand, for the student who manages her time well, it allows her to ask for an extension in cases where it makes sense (e.g. she has two other papers due that day) without making her feel as though she is asking for special treatment or that she is implying that my class has less priority.
It also cuts down on having to hear excuses. Finally, the quality of the papers that are turned in late are rarely better than the ones that are turned in on time - i.e., if there is an advantage to taking the extension I can assure you that it is not one that shows up in the grading. Well, not exactly, I do receive fewer papers that have one page of substance and four pages of filler. So, for those who take the extension, their papers might be better than they otherwise might have been. But those papers are rarely if ever better than the papers represented in the batch turned in on the due date.
The disadvantage is that the student has less time to respond to comments than she would have had, had she turned the paper in when it was due.
Any thoughts? Is this policy fair? Wise? What extension policies do you use?