Aims. We present a study of the Be/X-ray binary system V 0332+53 with the main goal of characterizing its behaviour mainly during the intermediate-luminosity X-ray event in 2008. In addition, we aim to contribute to the understanding of the behaviour of the donor companion by including optical data from our dedicated campaign starting in 2006. Methods. V 0332+53 was observed by RXTE and Swift during the decay of the intermediate-luminosity X-ray outburst of 2008, and with Suzaku before the rising of the third normal outburst of the 2010 series. In addition, we present recent data from the Spanish ground-based astronomical observatories of El Teide (Tenerife), Roque de los Muchachos (La Palma), and Sierra Nevada (Granada), and since...