Not in my class. But I have developed a type of compromise: you have until the day before I hand in my grades to submit any and all major writing assignments from the semester. Now, I don't go advertising this policy on my syllabus or in class. But nor do I advertise any penalty for late work. In my writing class especially, the deadlines are built into the syllabus, but the deadlines are preceded by in-class exercises and homework that guides them through a process for writing their papers. If you attended class and did all of the in-class and homework, your paper will be ready by the deadline (not to mention be a much more polished piece of writing).
But my students always seem to have excuses. Some are valid (freshmen especially seem to end up in the hospital due to the fact that they have taken really poor care of themselves during the semester). Some are suspect (your friend was in the hospital, computer virus, had to go home to babysit). Other are outright ridiculous (I didn't know we had a paper due, I didn't understand it, I swear I emailed it to you because I don't have any money left to print it). I'm tired of trying to figure out who is lying, who is trying to take advantage of me, and who really needs the extra time because of circumstances beyond their control. So, while it's better for my students to hand things in according to the schedule, at the end of the day, as long as they get it in to me before my grades are due, that's fine.
I have this policy in part because of karma; I was a terrible student as an undergraduate, and I rarely handed in assignments on time. I used every excuse in the book and sometimes didn't even bother offering one at all. But all of my professors allowed me to hand in my work and gave me full credit, however grudgingly. I can't help but smile inside when my undergrads come in, begging to be able to hand in their papers just a little late. Take your time, don't make yourself sick with stress and worry, and just hand it in to me when you have it done.
Is this an accurate reflection of real life? Probably not. Real life has hard and fast deadlines that need to be respected or else there will be some very real and potentially serious consequences. Don't ever miss an application deadline, and if your boss asks you for something by a certain day or time, you'd better make sure you do it. But in real life, there are always backup plans that can be put in place in oder to be able to mitigate the negative consequences of unforeseen events: work assignments can be handed off, divided up, or reassigned if you really cannot complete the work. There is also something to be said about the ability to say no, knowing when you have enough (or too much) work already, and thus telling your boss that if s/he wants it done well, they should assign it to someone else or give more time. But school doesn't allow for such flexibility. You are assigned work in each class, almost without regard to what else is being asked of you, and expected to get it done.
I know that students need to learn time management as well as the ability to take responsibility for their (often stupid) choices. But this is the beauty of my system: the students who really want to do well (and typically have a legitimate reason for missing the deadlines) will take the extra time, come and see me to talk about what they missed, and turn in their work in a reasonable timeframe, not falling so far behind that they now owe two or more major pieces of writing. Everyone else will keep putting off their work, scrambling at the end of the semester to hand something, anything, in to me to grade. And the work that they do hand in is rarely, if ever, good enough to earn a passing grade. Because they missed the process, the work is sloppy, and often doesn't even meet the assignment requirements. The students work harder than they have all semester in a desperate attempt to pass a class they put off, only to (usually) fail anyway.
And those students who do manage to hand in work that's good enough to pass the class? Good for them. When they become a professor later on in life (like I did), hopefully they'll pay it forward as well. But I also know that, one day, what they have done in the past won't work anymore. I also know that it is only then that they will learn the lesson. And those students who participated in the process? They are rewarded with a relatively stress-free semester (at least for my class) and a good grade.
I've always tell my students: I've got carrots and I've got sticks. Pick the one that works best for your motivation.