Willie McCovey, 79, is a former first baseman for the San Francisco Giants who played in the major leagues from 1959 to 1980. He hit 521 career home runs and was inducted into the Baseball Hall of Fame in 1986. He spoke with Marc Myers.

The South of my youth in the 1940s was strictly segregated. I grew up in Mobile, Ala., and as long as we stayed in our neighborhood, we were fine. But you still had to deal with the indignities. I remember a white fellow in his 20s coming to our house and addressing my father as “boy.” That...