Control of the COVID-19 pandemic requires significant changes in people's health behaviors. We offer this multidisciplinary perspective on the extent of compliance with social distancing recommendations and on coping with these measures around the globe in the first months of the pandemic. We present descriptive data from our survey of 17,650 respondents across 18 countries and territories in June 2020. The majority of respondents worried about contracting the virus. Nearly all engaged in at least some preventive behaviors, particularly handwashing, mask wearing, and avoiding social events. Most reported that it would be difficult to continue these behaviors for more than a few months, and about half reported feeling more anxious since the start of the pandemic. Commonly reported coping behaviors included news consumption, watching television, and sleeping. Our cross-national study highlights areas for developing and implementing health behavior interventions in the global fight to stop the spread of COVID-19.