Like Teachtoscrap, I keep copies of the list of students in my class (see attachment), so I (or a student) can easily and quickly check off who turned in what. My students love to help with this. I keep the list attached to the stack of papers. If I'm not near my computer to enter grades, I can put the grade on the checklist too to put in the electronic grade book later.
Rick Morris wrote a book called New Management
that has lots of fantastic techniques for reducing the time we spend on these kinds of things. I use many of his ideas in my classroom.