This study explores the relationship between several personal religion-related variables and social behaviour, using three paradigmatic economic games: the dictator (DG), ultimatum (UG), and trust (TG) games. A large carefully designed sample of the urban adult population in Granada (Spain) is employed (N = 766). 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) intensity of religiosity, measured by active participation at church services; and (iii) conversion 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. While the results partially support the notion of religious pro-sociality, on the other hand, they also highlight the importance of closely examining the multidimensional nature of both religiosity and pro-social behaviour.