I never accept late work. For me, late work is a slippery slope, if it's accepted 5 minutes late, then is 1 hour ok? What about 2 hours? What about 1 day because of a "broken printer"?
This policy is one to which I adhere because I believe it prepares students for life in the real world. When I worked as a technical writer, I was not allowed to submit late work, regardless of the reason (valid or not). There was no "partial credit."
Though I was initially branded "strict"--students have really come to respect me and my policy.