Cepheids in open clusters (cluster Cepheids: CCs) are of great importance as zero-point calibrators of the Galactic Cepheid period-luminosity relationship (PLR). We perform an 8-dimensional all-sky census that aims to identify new bona-fide CCs and provide a ranking of membership confidence for known CC candidates according to membership probabilities. The probabilities are computed for combinations of known Galactic open clusters and classical Cepheid candidates, based on spatial, kinematic, and population-specific membership constraints. Data employed in this analysis are taken largely from published literature and supplemented by a year-round observing program on both hemispheres dedicated to determining systemic radial velocities of Cepheids. In total, we find 23 bona-fide CCs, 5 of which are candidates identified for the first time, including an overtone-Cepheid member in NGC 129. We discuss a subset of CC candidates in detail, some of which have been previously mentioned in the literature. Our results indicate unlikely membership for 7 Cepheids that have been previously discussed in terms of cluster membership. We furthermore revisit the Galactic PLR using our bona fide CC sample and obtain a result consistent with the recent calibration by Turner (2010). However, our calibration remains limited mainly by cluster uncertainties and the small number of long-period calibrators. In the near future, Gaia will enable our study to be carried out in much greater detail and accuracy, thanks to data homogeneity and greater levels of completeness.