University students are frequently exposed to residential dampness or mold (i.e., visible mold, mold odor, dampness, or water leaks), a well-known contributor to asthma, allergic rhinitis, and respiratory infections. This study aims to: (a) describe the prevalence of these respiratory diseases among university students; and (b) examine the independent contribution of residential dampness or mold to these diseases. An online survey was conducted in March 2014 among the 26,676 students registered at the Université de Sherbrooke (Quebec, Canada). Validated questions and scores were used to assess self-reported respiratory diseases (i.e., asthma-like symptoms, allergic rhinitis, and respiratory infections), residential dampness or mold, and covariates (e.g., student characteristics). Using logistic regressions, the crude and adjusted odd ratios between residential dampness or mold and self-reported respiratory diseases were examined. Results from the participating students (n = 2097; response rate: 8.1%) showed high prevalence of allergic rhinitis (32.6%; 95% CI: 30.6–34.7), asthma-like symptoms (24.0%; 95% CI: 22.1–25.8) and respiratory infections (19.4%; 95% CI: 17.7–21.2). After adjustment, exposure to residential dampness or mold was associated with allergic rhinitis (OR: 1.25; 95% CI: 1.01–1.55) and asthma-like symptoms (OR: 1.70; 95% CI: 1.37–2.11), but not with respiratory infections (OR: 1.07; 95% CI: 0.85–1.36). Among symptomatic students, this exposure was also associated with uncontrolled and burdensome respiratory symptoms (p < 0.01). University students report a high prevalence of allergic rhinitis, asthma-like symptoms and respiratory infections. A common indoor hazard, residential dampness or mold, may play a role in increasing atopic respiratory diseases and their suboptimal control in young adults. These results emphasize the importance for public health organizations to tackle poor housing conditions, especially amongst university students who should be considered “at-risk”.