Regulation of harmful content on the Internet is a soaring problem in the expansion of the information society, and it is being discussed in different European countries. Therefore, it is important to discuss the issue of being safe online: to do research on what children think about when using the Internet, threats experienced while online, to discuss ways of recognising and protecting children from online threats (such as cyber bullying, bullying, abuse, temptations with purpose of sexual harassment, leaking of personal information, spreading, harmful and illegal Internet content, etc.). The research objective of this paper is to present the opinion of gymnasium students on using the Internet, online social networks and likely experienced threats. The methodology—opinion research of the gymnasium students, which was carried out 17–21 December 2012; an analysis of professional target publications and a questionnaire survey were also applied. Analysis of the research findings was based on the analysis methods of quantity analysis (descriptive) and analysis of quality content. Statistical findings were analysed applying the software “Statistical Package for the Social Sciences (SPSS) 21.0 for Windows.” According to the research of student opinion, it was revealed that the most common student online activities are browsing of chat websites, exchange of videos and other material, viewing, listening and participating in social networks, whereas erotica and viewing of pornography are the rarest activities and are unimportant for students. Online social networks are especially popular among students, as most interviewed students (95.3%) have their own profile in social networks. Students mostly visit social networks to communicate, to make friends (77.1% of respondents), however, every second student (60.7%) visits them just to spend time, which can be assumed about the problems of students’ leisure time. The vast majority of students think that they have sufficient knowledge and skills to protect themselves on the Internet, however, thinking does not protect from possible online threats and dangers. More than half of students keep their online profiles restricted, they can be only viewed by friends, and every third student keeps the profile partly restricted; however, every second student invites as friends strangers, friends of friends and easily share and spread personal information in the social networks: they reveal their surname (94.5%), upload photos where their face is visible (87.2%), indicate the name of the school that they attend (84.1%) and their real age (72.2%). Although students think that they limit access to their personal information, their insecure actions lead to them experiencing threats. Boys more often than girls tend to set their profile as public and tend to reveal more information in their profile, as compared to girls. They point out their hobbies, free-time activities, mobile phone number, home address, family relationships; the result of this is that boys are more likely to receive abusive messages than girls. Most students can name various threats and dangers that can be found online, in social networks; more than half of respondents claim that in social networks there are some topics that make youngsters uncomfortable. The vast majority of students think that sexual harassment is possible in social networks, the threat of publicity of personal photos and videos exists as well, there is likely to be incitement due to nationality, race, religion, customs and traditions etc. Because of easily published personal data it can be assumed that students do not understand the real danger of threats, as they think that these threats are “unreal” and cannot exist in the real world. It has been defined that students, if their rights were violated, would ask for help from their parents (60%) or friends (42.4%). However, almost one fifth of students (18.8%) would rather not ask for any help instead of asking a social educator, psychologist, teachers or class tutors. According to the research carried out it is recommended: to organize at the gymnasium constantly various prevention events to discuss facing threats on the Internet and in social networks, where lecturers could be not only from competitive professionals, but also trustworthy experienced people (ex. students or graduates). Teachers and students should aim for generous and mutual cooperation, association, respect and rely on each other so that a student facing some struggles could find a professional educator to help him/her.