Blue straggler stars (BSSs) are the most blue and massive stars in a cluster formed via binary or higher-order stellar interactions. We created a catalogue of BSSs in Galactic open clusters using Gaia DR2 data. Among the 670 clusters older than 300 Myr, we identified 868 BSSs in 228 clusters and 500 BSS candidates in 208 clusters. In general, all clusters older than 1 Gyr and massive than 1000 Msun have BSSs. The average number of BSSs increases with cluster age and mass, and there is a power-law relation between the cluster mass and the maximum number of BSSs in the cluster. We introduce a term, fractional mass excess (Me), for BSSs. We find that at least 54% of BSSs have Me<0.5 (likely to have gained mass through a binary mass transfer (MT)), 30% in the 0.5<Me<1.0 range (likely to have gained mass through a merger) and up to 16% with M4>1.0 (likely from multiple mergers/MT). Furthermore, we also find that the percentage of low Me BSSs increases with age, beyond 1–2 Gyr, suggesting an increase in formation through MT in older clusters. The BSSs are radially segregated, and the extent of segregation depends on the dynamical relaxation of the cluster. The statistics and trends presented here are expected to constrain the BSS formation models in open clusters.