The present study was aimed at establishing behavioral differences between three inbred mouse strains (129S2/SvHsd, C57BL/6JOlaHsd, FVB/NHsd) and two F1 hybrid lines derived from them (129×C57BL/6 and 129×FVB). The choice of the given strains was based on the frequent use of these mice in transgenic research. For the behavioral phenotyping, we employed a test battery consisting of the following models: elevated plus-maze (EPM), open field (OF), light–dark exploration, spontaneous locomotor activity, rota-rod (RR), Porsolt's forced-swimming test (FST), and Morris water task. Significant variations between the strains were established in all tests. Anxiety-like behavior was more pronounced in the 129S2/Sv and 129×C57BL/6 mice, the FVB/N mice were spontaneously hyperactive, the best coordination ability was demonstrated by the C57BL/6 and 129×C57BL/6 groups. A good performance in the learning test was established in both hybrid lines and the 129S2/Sv mice, whereas the well-known visual impairment of the FVB strain was confirmed by low performance in spatial and non-spatial tasks. Differences related to the gender were revealed occasionally; most importantly, 129×C57BL/6 males had a higher anxiety level than their female counterparts in the EPM. Several other gender dissociations suggest the strain and task specificity. In conclusion, we would like to highlight the importance of the genetic background and gender of mice for the molecular biological and pharmacological studies and also the need for well-established testing protocols to obtain wide information at the first stage of behavioral screening of genetically modified mice.