  We present a catalogue of 507 cataclysmic variables (CVs) observed in SDSS I
to IV including 70 new classifications collated from multiple archival data
sets. This represents the largest sample of CVs with high-quality and
homogeneous optical spectroscopy. We have used this sample to derive unbiased
space densities and period distributions for the major sub-types of CVs. We
also report on some peculiar CVs, period bouncers and also CVs exhibiting large
changes in accretion rates. We report 70 new CVs, 59 new periods, 178
unpublished spectra and 262 new or updated classifications. From the SDSS
spectroscopy, we also identified 18 systems incorrectly identified as CVs in
the literature. We discuss the observed properties of 13 peculiar CVS, and we
identify a small set of eight CVs that defy the standard classification scheme.
We use this sample to investigate the distribution of different CV sub-types,
and we estimate their individual space densities, as well as that of the entire
CV population. The SDSS I to IV sample includes 14 period bounce CVs or
candidates. We discuss the variability of CVs across the Hertzsprung-Russell
diagram, highlighting selection biases of variability-based CV detection.
Finally, we searched for, and found eight tertiary companions to the SDSS CVs.
We anticipate that this catalogue and the extensive material included in the
Supplementary Data will be useful for a range of observational population
studies of CVs.
