Cyclodextrins (CDs) are cyclic oligosaccharides that contain a relatively hydrophobic central cavity and a hydrophilic outer surface. They are widely used to form non-covalent inclusion complexes with many substances. Although such inclusion complexes typically exhibit higher aqueous solubility and chemical stability than pure drugs, it has been shown that CDs can promote the degradation of some drugs. This property of stabilizing certain drugs while destabilizing others can be explained by the type of CD used and the structure of the inclusion complex formed. In addition, the ability to form complexes of CDs can be improved through the addition of suitable auxiliary substances, forming multicomponent complexes. Therefore, it is important to evaluate the effect that binary and multicomponent complexes have on the chemical and physical stability of complexed drugs. The objective of this review is to summarize the studies on the stabilizing and destabilizing effects of complexes with CDs on drugs that exhibit stability problems.