Attending the veterinary clinic is an integral part of the physical welfare of every companion dog. However, some dogs experience their veterinary visits negatively, which poses a risk of injury to the veterinary staff, their guardian (owner) and themselves. It may also influence the regularity of non-urgent veterinary appointments. To date there have been conflicting reports relating to the proportion of dogs that show fear during their veterinary visits. In this study, we explored the risk factors associated with fear during veterinary examination and in novel situations (including first time at the veterinary clinic) from 26,555 responses in the Canine Behavioral Assessment and Research Questionnaire database. According to their guardians, 41% of companion dogs displayed mild to moderate fearful behaviour when examined by a veterinarian, and 14% exhibited severe or extreme fear. A similar trend was observed with dogs responding fearfully when in unfamiliar situations, including the dog's first time at the veterinary clinic. Chi-squared tests showed every bivariate relationship between fear and the environmental and demographic factors measured was significant (p < 0.05). The most important predictors of fear in a veterinary examination were, in order: the dog's breed group (27.1%), their history of roles or activities (16.7%), where they were sourced (15.2%), their weight (12%), the age of other dogs in the household (9.5%) and dog owner experience (6.3%). However, combined these risk factors only explain a total of 7% of variance of fear observed during veterinary examination. This suggests that fear exhibited during veterinary visits is common in dogs, but that the environment or human-animal interactions are likely to contribute more to prevalence and severity of this problem than the demographic factors measured here. We conclude by highlighting opportunities for future research aimed at facilitating less stressful veterinary visits for dogs and their guardians.