Examining today’s tourism, we should recognize the appearance and intensification of socially and environmentally undesirable side effects of tourism. A change is necessary in order to maintain the popularity of tourism and to develop it further. This change must take place both in terms of supply and consumer demand. In the present study, we examine the extent to which the Hungarian population is open to demonstrating environmentally conscious and responsible consumer behaviour during their travels. The diverse consumer behaviours of the generations are well known, but in the case of tourism, this is a somewhat less researched area. The current study was carried out to explore these generational differences. As part of the research, we conducted an online survey of 1,085 respondents in April and May of 2018 with the aim of examining the attitudes of the Hungarian population toward tourism, focusing on the generational perspective. In this paper, we analyse the results of some important manifestations of responsible tourism and the attitudes of the Hungarian population toward environmental issues. In our opinion, the study is also relevant because many tourist destinations are already struggling with the negative effects of overtourism, so it is critical that we explore whether there is willingness among tourists to adopt more environmentally conscious and responsible consumer behaviour patterns. Employing the core research data, we performed a cluster analysis, with the help of which we attempted to characterize a range of consumer groups.