Web search engines have become the dominant tools for finding information on the Internet. Owing to their popularity, users of all educational backgrounds and professions use them for a wide range of tasks, from simple look-up to rather complex information-seeking needs. This paper presents the results of a study that investigates the behavioural search characteristics of ordinary Web search engines users. The aim of the study was to investigate (1) what makes complex search tasks distinct from simple search tasks and whether it is possible to find simple measures for describing their complexity, and (2) whether successful searchers show different search behaviours than unsuccessful searchers and whether good searchers can be identified via simple measures. The study included 56 ordinary Web users who carried out a set of 12 search tasks using current commercial search engines. Their behaviour was logged with the Search-Logger tool. The results confirm that the behaviour in the case of complex search tasks has significantly different inherent characteristics than in the case of simple search tasks. This can be proven by using simple measures such as task time, number of queries, or number of browser tabs used. We also observed that it is difficult to distinguish successful from unsuccessful search behaviour simply by using these measures. The implications of our findings for search engine vendors are discussed. The results of this study with a sample of ordinary users are insofar unique as they are valid for a wider population while most studies in the field are usually done using convenience samples such as university students.