Establishing Expectations and Standards
To minimize the possibility of confusion and to protect yourself in the event of disputes, it's wise to establish your expectations and grading policies for each assignment, present these to the students in written form, and follow them as much as possible when grading. This is more true of papers than of exams, although it doesn't hurt to spend a couple of minutes during the section prior to an exam outlining the kinds of things that characterize a successful exam.

Grading Rubric
You might consider creating a grading rubric to pass out to your students. This makes what is often a subjective activity appear more objective to your students. It will also help you clarify in your own mind the distinguishing features of successful papers.

Most rubrics take one of two forms: (1) The Top-Down Model and (2) the Average-Up Model. The former begins with an A, describing the ideal paper, and works its way down, defining lower-level papers by what they lack. The latter begins with a C or Average paper, which meets the minimum criteria of the assignment (or alternatively a B- or okay paper) and defines higher and lower-level papers in relation to this norm, either as they surpass or fail to meet these criteria. As an approach to grading, both of these models have their good and bad features. If you begin by seeing all papers as A's, you give the student the benefit of the doubt, but you may also then tend to see only what is wrong with the paper. On the other hand, if you begin from the position that all papers are C's, you may begin to see everything as average and only very grudgingly give A's.

Sample Rubric Handout