Forer effect: The tendency of people to rate statements about themselves as highly and uniquely accurate, even when the statements are vague and could apply to many people. (Newspaper horoscopes are the classic example.) Also called the personal validation fallacy, the phenomenon is named for psychologist Bertram R. Forer (1914-2000), who gave identical personality evaluations to a group of students and asked them to rate their evaluation on a scale from zero to five. The average score was 4.26. The experiment has been repeated many times; the average remains about 4.2.
Hat tip to Nancy R. Callahan of Nancy's Baby Names, who introduced me to the term.