Aims. This is the first of a series of papers in which we present the results of a long-term photometric monitoring project carried out at Catania Astrophysical Observatory aimed at studying magnetic activity in late-type components of close binary systems, its dependence on global stellar parameters, and its evolution on different time scales from days to years. In this first paper, we present the complete observation dataset and new results of an investigation into the origin of brightness and color variations observed in the well-known magnetically active close binary stars: AR Psc, VY Ari, UX Ari, V711 Tau, EI Eri, V1149 Ori, DH Leo, HU Vir, RS CVn, V775 Her, AR Lac, SZ Psc, II Peg and BY Dra Methods. About 38 000 high-precision photoelectric nightly observations in the U, B and V filters are analysed. Correlation and regression analyses of the V magnitude vs. U-B and B-V color variations are carried out and a comparison with model variations for a grid of active region temperature and filling factor values is also performed. Results. We find the existence of two different patterns of color variation. Eight stars in our sample: BY Dra, VY Ari, V775 Her, II Peg, V1149 Ori, HU Vir, EI Eri and DH Leo become redder when they become fainter, as is expected from the presence of active regions consisting of cool spots. The other six stars show the opposite behaviour, i.e. they become bluer when they become fainter. For V711 Tau this behaviour could be explained by the increased relative U-and B-flux contribution by the earlier-type component of the binary system when the cooler component becomes fainter. On the other hand, for AR Psc, UX Ari, RS CVn, SZ Psc and AR Lac the existence of hot photospheric faculae must be invoked. We also found that in single-lined and double-lined binary stars in which the fainter component is inactive or much less active the V magnitude is correlated to B-V and U-B color variations in more than 60% of observation seasons. The correlation is found in less than 40% of observation seasons when the fainter component has a non-negligible level of activity and/or hot faculae are present but they are either spatially or temporally uncorrelated to spots.