Objectives: To investigate the general population's view on artificial intelligence (AI) in medicine with specific emphasis on 3 areas that have experienced major progress in AI research in the past few years, namely radiology, robotic surgery, and dermatology. Methods: For this prospective study, the April 2020 Online Longitudinal Internet Studies for the Social Sciences Panel Wave was used. Of the 3117 Longitudinal Internet Studies For The Social Sciences panel members contacted, 2411 completed the full questionnaire (77.4% response rate), after combining data from earlier waves, the final sample size was 1909. A total of 3 scales focusing on trust in the implementation of AI in radiology, robotic surgery, and dermatology were used. Repeated-measures analysis of variance and multivariate analysis of variance was used for comparison. Results: The overall means show that respondents have slightly more trust in AI in dermatology than in radiology and surgery. The means show that higher educated males, employed or student, of Western background, and those not admitted to a hospital in the past 12 months have more trust in AI. The trust in AI in radiology, robotic surgery, and dermatology is positively associated with belief in the efficiency of AI and these specific domains were negatively associated with distrust and accountability in AI in general. Conclusions: The general population is more distrustful of AI in medicine unlike the overall optimistic views posed in the media. The level of trust is dependent on what medical area is subject to scrutiny. Certain demographic characteristics and individuals with a generally positive view on AI and its efficiency are significantly associated with higher levels of trust in AI.