Health risk factors such as body mass index (BMI) and serum cholesterol are associated with many common diseases. It often remains unclear whether the risk factors are cause or consequence of disease, or whether the associations are the result of confounding. We develop and apply a method (called GSMR) that performs a multi-SNP Mendelian randomization analysis using summary-level data from genome-wide association studies to test the causal associations of BMI, waist-to-hip ratio, serum cholesterols, blood pressures, height, and years of schooling (EduYears) with common diseases (sample sizes of up to 405,072). We identify a number of causal associations including a protective effect of LDL-cholesterol against type-2 diabetes (T2D) that might explain the side effects of statins on T2D, a protective effect of EduYears against Alzheimer's disease, and bidirectional associations with opposite effects (e.g., higher BMI increases the risk of T2D but the effect of T2D on BMI is negative).