High bed occupancy rates have been considered a matter of reduced patient comfort and privacy and an indicator of high productivity for hospitals. Hospitals with bed occupancy rates of above 85 percent are generally considered to have bed shortages. Little attention has been paid to the impact of these shortages on patients' outcomes. We analyzed all 2.65 million admissions to Danish hospitals' departments of medicine in the period 1995-2012. We found that high bed occupancy rates were associated with a significant 9 percent increase in rates of in-hospital mortality and thirty-day mortality, compared to low bed occupancy rates. Being admitted to a hospital outside of normal working hours or on a weekend or holiday was also significantly associated with increased mortality. The health risks of bed shortages, including mortality, could be better documented as a priority health issue. Resources should be allocated to researching the causes and effects of bed shortages, with the aim of creating greater interest in exploring new methods to avoid or reduce bed shortages.