This study explores the effect of several personal religion-related variables on social behaviour, using three paradigmatic economic games: the dictator (DG), ultimatum (UG), and trust (TG) games. A large carefully designed sample of a Spanish urban adult population (N=766) is employed. From participants' decisions in these games we obtain measures of altruism, bargaining behaviour and sense of fairness/equality, trust, and positive reciprocity. Three dimensions of religiosity are examined: (i) religious denomination; (ii) the intensity of religiosity, measured by active participation at church services; and (iii) converting out into a different denomination than the one raised in. The major results are: (i) individuals with "no religion" made decisions closer to rational selfish behaviour in the DG and the UG compared to those who affiliate with a "standard" religious denomination; (ii) among Catholics, intensity of religiosity is the key variable that affects social behaviour insofar as religiously-active individuals are generally more pro-social than non-active ones; and (iii) the religion raised in seems to have no effect on pro-sociality, beyond the effect of the current measures of religiosity. Importantly, behaviour in the TG is not predicted by any of the religion-related variables we analyse. Given the accelerating share of "no religion" individuals (in Europe and elsewhere) and the large influx of immigrants – who tend to be more religiously active compared to the native populations – our findings have significant implications for the future pro-sociality patterns in Europe.