This article presents, with reference to the development of European financial markets affected by crises, a view on the relationship between competition among banks and the stability of the banking system and of the entire economy, the maintenance of which is as a goal of public policy of primary importance. A certain degree of instability is caused by the nature of banking activity; another source of instability may be a result of competition. The interconnection between the level of competition in the banking sector and the sector’s stability produces various outcomes: usually, increased competition causes the banking system to become more unstable, but can sometimes make it more stable, depending on the particular conditions of the market. Various situations of banking market development are discussed and described by modeling banking behavior. The main instruments of the regulation of banking market development and competition are described as well as their use in the European market in times of crisis.