Setting Your Late Work Policy
You probably should include your late-work policy on your syllabus, articulate it in class on the first day, and include it with every assignment sheet you distribute. Some instructors assess penalties on late work, often increasing them over time. Some refuse to accept late submissions unless students make explicit arrangements for an extension in advance of the due date. You should set a policy that addresses your needs and enables learning. Keep in mind that any policy will require that you keep accurate records.
If you require students to submit work electronically, either by email enclosures or via an online dropbox, you will have an accurate record of when the work was submitted. Keeping emails over an entire term also helps. Be clear and consistent and repeat your policy frequently.