Optimal prediction of the values of regionalized variables or the means of random fields is often accomplished by using kriging methods. These methods rely on satisfactory estimation of the underlying spatial semivariograms and the fitting of semivariogram models. Individual observations can have a dramatic effect on sample semivariograms because each observation is used many times in the calculation of the semivariogram values. Anomalous observations may induce spikes, give rise to sharp peaks, shift the entire semivariogram upwards, or induce a linear trend in the sample semivariogram plot. In this article, all four of these outlier-induced aberrations are illustrated using two widely differing datasets: one on soil nutrient concentrations, the other on global temperatures. A number of graphical techniques are used to locate individual influential data values and spatially cohesive clusters of influential values. In addition, quantitative methods for detecting influential observations are discussed.