Many things in life must be done both well and on time. (Consider the decision-making of a physician in an emergency room.) You should always strive to do both. Nevertheless, sometimes that is impossible, and so we must compromise on either quality or timeliness. (This is what real-time systems are about, and it is one aspect of my research.)
My standard late policy is intended to encourage students to hand work in on time, but not to be a disaster if you're a day or two late. I think students can learn more by doing a job well, even if the late penalty costs them a little, than by turning in a poor job on time.
The following policy is what I enforce unless otherwise stated in the course syllabus. I will penalize your assignment ten points (one letter grade) per day. Obviously, it is pointless to turn something in ten or more days late; indeed, it's hardly worth bothering to turn something in a week late. For something that is half a day late, it might be only five points, but after something is twenty-four hours late, let's not quibble over whether it's 2.5 or 2.75 days late.
For programming assignments and other "soft copy", the time you turn it in is the time of the email message to me or the timestamp on the file in the drop folder.
Anything handed in on paper will be turned in at the beginning of class.
The end of the semester is a busy time for all of us, and I cannot do a good job grading assignments and preparing exams if I am grading a flurry of late assignments. Therefore, the absolute last day to turn in assignments is the last day of classes. If an assignment is due on the last day of classes, that means it may not be turned in late. I'm sorry, but only in unusual cases, where you have gotten my permission in advance, will I accept anything after midnight of the last day of classes.