Some common errors exhibited by students in interpreting graphs in physics are illustrated by examples from kinematics.  These are taken from the results of a descriptive study extending over a period of several years and involving several hundred university students who were enrolled in a laboratory-based preparatory physics course.  Subsequent testing indicated that the graphing errors made by this group of students are not idiosyncratic, but are found in different populations and across different levels of sophistication.  This paper examines two categories of difficulty identified in the investigation:  difficulty in connecting graphs to physical concepts and difficulty in connecting graphs to the real world.  Specific difficulties in each category are discussed in terms of student performance on written problems and laboratory experiments.  A few of the instructional strategies that have been designed to address some of these difficulties are described.