Biomaterials are in high demand due to the increasing geriatric population and a high prevalence of cardiovascular and orthopedic disorders. The combination of additive manufacturing (AM) and biomaterials is promising, especially towards patient-specific applications. With AM, unique and complex structures can be manufactured. Furthermore, the direct link to computer-aided design and digital scans allows for a direct replicable product. However, the appropriate selection of biomaterials and corresponding AM methods can be challenging but is a key factor for success. This article provides a concise material selection guide for the AM biomedical field. After providing a general description of biomaterial classes—biotolerant, bioinert, bioactive, and biodegradable—we give an overview of common ceramic, polymeric, and metallic biomaterials that can be produced by AM and review their biomedical and mechanical properties. As the field of load-bearing metallic implants experiences rapid growth, we dedicate a large portion of this review to this field and portray interesting future research directions. This article provides a general overview of the field, but it also provides possibilities for deepening the knowledge in specific aspects as it comprises comprehensive tables including materials, applications, AM techniques, and references.