The study presented in this paper explored the relationships between participant personality, perceived robot personality and preferences for particular robot appearances. The participants (N=77) watched 3 videos of a HRI situation in which the appearance of the robot was altered to appear more or less anthropomorphic. Participant personality was assessed using the Big Five Domain Scale, while Robot Personality was measured using 5 items based on the traits from the Big Five Model. The results reveal that low Emotional Stability and Extraversion scores are related to preferences for mechanical robot appearances. Results for perceived robot personality suggest that participants clearly differentiated between the different robots on the dimensions of Extraversion, Agreeableness and Intelligence, but did not differentiate strongly between them on the Emotional Stability dimension.