Relative proper motions have been determined for 1127 stars in the field of the open cluster NGC 188 from plates spanning a 60-year interval, taken with the 76-cm Thaw refractor of the Allegheny Observatory. Special attention has been paid to the corrections for systematic errors as a function of magnitude and color, and to the treatment of membership probabilities for stars with different proper-motion errors. The study is complete to a magnitude B = 16.2. Also some stars brighter than B = 12.5 were eliminated from the study because of the large uncertainty in estimating the magnitude equation at the bright end. The final relative proper motions have an accuracy of 0.5 mas/yr for well-exposed stars. From the cluster membership probabilities based on proper motions we obtain 360 cluster members, enabling us to better define the color-magnitude diagram. We provide a list of highly probable candidate blue stragglers in addition to the sample proposed by Eggen & Sandage (1969). In order to investigate mass segregation, we have analyzed the spatial distribution of the possible blue stragglers. Based on our proper-motion probabilities the spatial cumulative distributions show that the blue stragglers are not more centrally concentrated than the red giants.