In the modern world, the number of new users of computer systems and Internet users is growing rapidly. It can be said that the Internet and all its systems and services arising from it were almost overnight permeated to all spheres of human life. The world has become almost unthinkable without the computer systems and the Internet. To better understand the importance of the Internet, but also disadvantages that it entails, it is necessary to be familiar with its origin and development, applications, services, and end users. They are important component of a computer system which, as its ultimate user can influence with their behavior to the level of its security. Although most of working papers are focused on improving the computer system at program level by the service provider, end users are being ignored as an essential element of this system. This paper deals with precisely this issue and emphasizes its importance. Through a survey, carried out in a particular sample of people, the habits and behavior of the computer system users and the Internet users were surveyed in order to assess their awareness of security issues and how themselves can influence them. After analyzing the survey, it can be concluded that users generally are familiar with the computer systems and the dangers that may arise from its misuse. On the other hand, they are often careless, insufficiently attentive and aware and do not attach enough importance to keeping secure their personal data and documents. They often think that the potentially risk will never happen to them. It is extremely important to emphasize the need for better educating users about security issues on which they can have a negative impact if they use it improperly, and they can potentially do harm to themself or others, either intentionally or unintentionally.