Artificial intelligence (AI) applications offer numerous opportunities to improve health care. To be used in the intensive care unit, AI must meet the needs of staff, and potential barriers must be addressed through joint action by all stakeholders. It is thus critical to assess the needs and concerns of anesthesiologists and intensive care physicians related to AI in health care throughout Europe. This Europe-wide, cross-sectional observational study investigates how potential users of AI systems in anesthesiology and intensive care assess the opportunities and risks of the new technology. The web-based questionnaire was based on the established analytic model of acceptance of innovations by Rogers to record 5 stages of innovation acceptance. The questionnaire was sent twice in 2 months (March 11, 2021, and November 5, 2021) through the European Society of Anaesthesiology and Intensive Care (ESAIC) member email distribution list. A total of 9294 ESAIC members were reached, of whom 728 filled out the questionnaire (response rate 728/9294, 8%). Due to missing data, 27 questionnaires were excluded. The analyses were conducted with 701 participants. A total of 701 questionnaires (female: n=299, 42%) were analyzed. Overall, 265 (37.8%) of the participants have been in contact with AI and evaluated the benefits of this technology higher (mean 3.22, SD 0.39) than participants who stated no previous contact (mean 3.01, SD 0.48). Physicians see the most benefits of AI application in early warning systems (335/701, 48% strongly agreed, and 358/701, 51% agreed). Major potential disadvantages were technical problems (236/701, 34% strongly agreed, and 410/701, 58% agreed) and handling difficulties (126/701, 18% strongly agreed, and 462/701, 66% agreed), both of which could be addressed by Europe-wide digitalization and education. In addition, the lack of a secure legal basis for the research and use of medical AI in the European Union leads doctors to expect problems with legal liability (186/701, 27% strongly agreed, and 374/701, 53% agreed) and data protection (148/701, 21% strongly agreed, and 343/701, 49% agreed). Anesthesiologists and intensive care personnel are open to AI applications in their professional field and expect numerous benefits for staff and patients. Regional differences in the digitalization of the private sector are not reflected in the acceptance of AI among health care professionals. Physicians anticipate technical difficulties and lack a stable legal basis for the use of AI. Training for medical staff could increase the benefits of AI in professional medicine. Therefore, we suggest that the development and implementation of AI in health care require a solid technical, legal, and ethical basis, as well as adequate education and training of users.