A number of studies have investigated the acceptance of conditionally automated cars (CACs). However, in the future, CACs will comprise of several separate Automated Driving Functions (ADFs), which will allow the vehicle to operate in different Operational Design Domains (ODDs). Driving in different environments places differing demands on drivers. Yet, little research has focused on drivers’ intention to use different functions, and how this may vary by their age, gender, country of residence, and previous experience with Advanced Driving Assistance Systems (ADAS). Data from an online survey of 18,631 car drivers from 17 countries (8 European) was used in this study to investigate intention to use an ADF in one of four different ODDs: Motorways, Traffic Jams, Urban Roads, and Parking. Intention to use was high across all ADFs, but significantly higher for Parking than all others. Overall, intention to use was highest amongst respondents who were younger (<39), male, and had previous experience with ADAS. However, these trends varied widely across countries, and for the different ADFs. Respondents from countries with the lowest Gross Domestic Product (GDP) and highest road death rates had the highest intention to use all ADFs, while the opposite was found for countries with high GDP and low road death rates. These results suggest that development and deployment strategies for CACs may need to be tailored to different markets, to ensure uptake and safe use.