Objectives: To investigate medication non-adherence and its determinants in diabetes, hypertension, and hyperlipidemia. Methods: In a multicenter, cross-sectional, non-interventional study, 518 diabetic, 721 hypertensive, and 463 hyperlipidemic patients were recruited, using consecutive sampling, in Greece during the COVID-19 pandemic. Medication adherence was measured with the Adherence to Refills and Medications Scale (ARMS). Multiple linear regressions with robust standard errors investigated the predictors of the ARMS summary score. Results: Perfect adherence was estimated at 16%, 12%, and 11%, and low adherence at 38.8%, 61.3%, and 66.7% in diabetes, hypertension, and hyperlipidemia, respectively. The factors that significantly increased the likelihood of non-adherence were the following: (a) lower age, female gender, no public health insurance, high perceived threat of illness, low satisfaction with physician consultations, shorter consultations, bad general health, fewer comorbidities, and type 2 diabetes; (b) male gender, not being married, low education, no public insurance, smoking, frequent drinking, shorter consultations, self-perceived inadequacy of knowledge, negative views of medication, presence of comorbidities, fewer medicines being used, and high blood pressure in hypertension; and (c) lower age, not being employed, smoking, frequent drinking, no public insurance, low satisfaction with consultations, negative views of medication, taking 3–4 medicines, high LDL, and low HDL and triglyceride levels in hyperlipidemia. Different curvilinear associations of adherence with BMI and exercise were also found. Conclusion: Medication non-adherence is very common in diabetes, hypertension, and hyperlipidemia. Strategies to improve adherence should consider the different determinants of non-adherence among patient groups.