Galaxies with polar rings (PRGs) are a unique class of extragalactic objects. Using these, we can investigate a wide range of problems, linked to the formation and evolution of galaxies, and we can study the properties of their dark haloes. The progress that has been made in the study of PRGs has been constrained by the small number of known objects of this type. The Polar Ring Catalogue (PRC) by Whitmore et al. and their photographic atlas of PRGs and related objects includes 157 galaxies. At present, there are only about two dozen kinematically confirmed galaxies in this PRG class, mostly from the PRC.We present a new catalogue of PRGs, supplementing the PRC and significantly increasing the number of known candidate PRGs. The catalogue is based on the results of the original Galaxy Zoo project. Within this project, volunteers performed visual classifications of nearly a million galaxies from the Sloan Digital Sky Survey (SDSS). Based on the preliminary classifications of the Galaxy Zoo, we viewed more than 40 000 images of the SDSS and selected 275 galaxies to include in our catalogue.Our SDSS-based Polar Ring Catalogue (SPRC) contains 70 galaxies that we have classified as 'the best candidates'. Among these, we expect to have a very high proportion of true PRGs, and 115 good PRG candidates. There are 53 galaxies classified as PRG-related objects (mostly galaxies with strongly warped discs, and mergers). In addition, we have identified 37 galaxies that have their presumed polar rings strongly inclined to the line of sight (seen almost face-on). The SPRC objects are, on average, fainter and are located further away than the galaxies from the PRC, although our catalogue does include dozens of new nearby candidate PRGs.The SPRC significantly increases the number of genuine PRG candidates. It might serve as a good basis for both a further detailed study of individual galaxies and a statistical analysis of PRGs as a separate class of objects.We have performed spectroscopic observations of six galaxies from the SPRC at the 6-m Big Telescope Alt-Azimuthal (BTA). The existence of polar rings was confirmed in five galaxies, and one object appeared to be a projection of a pair of galaxies. Adding the data from the literature, we can already classify 10 galaxies from our catalogue as kinematically confirmed PRGs.