Alcohol has a direct effect on blood coagulation and fibrinolysis. We studied how alcohol is related to common bleeding events (e.g., nose bleeding), as well as life-threatening bleeding events (e.g., hemorrhagic stroke) that required hospital care in the general population. We used data from The Copenhagen City Heart Study, 1991 to 1994 and 2001 to 2003. Baseline information on alcohol consumption and potential confounders was obtained by questionnaires, and participants were followed for incident bleeding events with nationwide registers until 2013. Among the 10,259 included participants, we observed 366 nose or other respiratory organ bleeding events, 149 hemorrhagic stroke events, 470 gastrointestinal bleeding events, 266 unspecified bleeding events, and 1088 any-bleeding events (composite endpoint) during follow-up. Compared to drinkers of 1–6 drinks per week, those drinking ≥35 drinks per week had a higher risk of hemorrhagic stroke [hazard ratio, 2.27 (1.14–4.55)] and non-variceal gastrointestinal bleeding [hazard ratio 2.04 (1.37–3.05)], whereas non-drinkers and drinkers of 7–13, 14–20, 21–27, and 28–34 drinks per week had not. Alcohol consumption was not associated with risk of nose or other respiratory organ bleeding or unspecified bleeding. For non-drinkers and drinkers of 7–13, 14–20, 21–27, 28–34, and 35 or more drinks per week, hazard ratios for the composite endpoint of any bleeding were 1.17 (95% CI: 0.99–1.37), 0.97 (95% CI: 0.81–1.15), 1.00 (95% CI: 0.80–1.26), 0.93 (95% CI: 0.69–1.25), 1.39 (95% CI: 1.00–1.94), and 1.83 (95% CI: 1.39–2.41) compared to drinkers of 1–6 drinks per week. In conclusion, drinking 35 or more drinks per week may be associated with a higher risk of hemorrhagic stroke and non-variceal gastrointestinal bleeding in the general population.