Cat domestication and selective breeding have resulted in tens of breeds with major morphological differences. These breeds may also show distinctive behaviour differences; which, however, have been poorly studied. To improve the understanding of feline behaviour, we examined whether behavioural differences exist among cat breeds and whether behaviour is heritable. For these aims, we utilized our extensive health and behaviour questionnaire directed to cat owners and collected a survey data of 5726 cats. Firstly, for studying breed differences, we utilized logistic regression models with multiple environmental factors and discovered behaviour differences in 19 breeds and breed groups in ten different behaviour traits. Secondly, the studied cat breeds grouped into four clusters, with the Turkish Van and Angora cats alone forming one of them. These findings indicate that cat breeds have diverged not only morphologically but also behaviourally. Thirdly, we estimated heritability in three breeds and obtained moderate heritability estimates in seven studied traits, varying from 0.4 to 0.53, as well as phenotypic and genetic correlations for several trait pairs. Our results show that it is possible to partition the observed variation in behaviour traits into genetic and environmental components, and that substantial genetic variation exists within breed populations.