(1) Background: Extracorporeal membrane oxygenation (ECMO) is increasingly used for acute respiratory failure with few absolute but many relative contraindications. The provider in charge often has a difficult time weighing indications and contraindications to anticipate if the patient will benefit from this treatment, a decision that often decides life and death for the patient. To assist in this process in coming to a good evidence-based decision, we reviewed the available literature. (2) Methods: We performed a systematic review through a literature search of the MEDLINE database of former and current absolute and relative contraindications to the initiation of ECMO treatment. (3) Results: The following relative and absolute contraindications were identified in the literature: absolute—refusal of the use of extracorporeal techniques by the patient, advanced stage of cancer, fatal intracerebral hemorrhage/cerebral herniation/intractable intracranial hypertension, irreversible destruction of the lung parenchyma without the possibility of transplantation, and contraindications to lung transplantation; relative—advanced age, immunosuppressed patients/pharmacological immunosuppression, injurious ventilator settings > 7 days, right-heart failure, hematologic malignancies, especially bone marrow transplantation and graft-versus-host disease, SAPS II score ≥ 60 points, SOFA score > 12 points, PRESERVE score ≥ 5 points, RESP score ≤ −2 points, PRESET score ≥ 6 points, and “do not attempt resuscitation” order (DN(A)R status). (4) Conclusions: We provide a simple-to-follow algorithm that incorporates absolute and relative contraindications to the initiation of ECMO treatment. This algorithm attempts to weigh pros and cons regarding the benefit for an individual patient and hopefully assists caregivers to make better, informed decisions.