Cats have grown in popularity as companion animals, but there are also people who strongly dislike them. Companion cats allowed to roam freely outdoors are seen by some as a nuisance. This paper, drawing on research conducted in Denmark, aims to quantify potentially conflicting attitudes to cats among the public that may feed into cat-related conflicts and controversies. Questionnaire data were collected from a representative sample of the Danish population (n = 2,003), where 21% (n = 415) owned cats and 79% (n = 1,588) did not. In all, 65% of respondents confirmed that they liked cats, 21% reported that they did not, and 14% were undecided. The main reasons for disliking cats concerned “behavior,” not hazards such as the spread of diseases and predation. Of the 21% of the surveyed Danes who reported that they currently had a cat in the household, 72% allowed their cat to roam outdoors. Sixty percent of the respondents did not perceive this as a problem. However, the potential for conflict was demonstrated by the fact that 27% of respondents regarded outdoor roaming as problematic. Of these, about a quarter saw free-roaming cats as a big problem and as a cause of strife between neighbors. Comparatively fewer of those who owned cats saw their animals as a cause of problems. Thus, only 12% of those owning outdoor cats thought that problems were caused when their cats defecated in a neighbor’s garden, which compares with the 17% of the total population who are bothered by other people’s cats defecating in their gardens. Our data show that while the majority of Danes believe cats should be allowed to roam in public spaces, a significant minority strongly dislikes cats and would prefer restrictions on roaming.