Banks, as financial institutions, usually represent the main financial intermediaries and consequently the most financial systems are characterized as a bank-centric. Stable and efficient financial system can substantially support a economic growth of a country. A deposit insurance system represents the protection of deposits against the loss of deposits in the event of secure cases, the preservation of confidential deposits and the contribution to the stability of the entire financial system. The topic of this paper relates to deposit insurance systems, their features and consequently and also advantages and disadvantages. The 2008 financial crisis has highlighted experts and the general population on the fragility of existing financial systems in the world, most of which were in Europe. The basic aim of this research is to analyze deposit insurance systems, with an emphasis on detailed analysis of their models, more specifically their advantages and disadvantages. The deposit insurance system, as one of the measures that affects the stability of the banking and financial system as a whole, has the task of "restoring" the trusted confidence of depositors through adequate protection that applies. Along this path, in pursuit of its primary objective, the deposit insurance system has three pitfalls: moral hazard, negative selection and principal agent problems.