What's a good way to prevent students from saying I lost their paper? As a teacher, I've often had students say that they turned in an assignment, but that because I don't see it, grade it, and return it back to them, that I must have lost their papers/assignments. I tend to be disorganized at times, so it's hard for me to confidently say that I really haven't lost their papers. To make matters worse, I have lost a student paper or two over the years only to find it weeks later. 

How should I respond? 

Notes:


Many have noted electronic submission. I'm assuming for this question that students turn in something physical that I could theoretically lose. ;-) This also allows this question to be applicable to schools that may not use electronic submission.
First, get organized.

You need a good defence. Make sure that you are not at fault. 

What I've done is to put student assignments in a folder and keep it entirely separate from any other papers I have. When I bring their assignments home, I transport them in a plastic bag to further distinguish them and prevent papers from falling out somehow. For situations where the class turns in lots of assignments and students don't always pick up their graded assignments, papers can get out of order, so I make sure to keep each assignment in a separate folder, or I put all graded assignments in a single stack alphabetized by last name. I know with full certainty that students' assignments are in my "to-grade" folder, or my "to-return" folder, and nowhere else. 

Second, respond to the student

If they say you've lost their paper, give them the benefit of the doubt by looking through your stack. If it's not there, you know it won't be anywhere else, short of a devious third-party intervention, and you can tell them so. :-)

Alternatives


Use an electronic submission dropbox (e.g. Blackboard, D2L, etc.). 


You could have students email their assignments to you, but there's always the possibility that it gets caught in your spam filter. If you did this, you should send them an email ASAP to confirm that you received their submission. 

Keep all papers in a single room: never take them home to grade, etc.
Keep a list of students who submitted their work as they turn it in. 
Scan in assignments, keep an electronic copy and send the copy to students (idea from @MadMyche, in the comments below).