The issue of point prevalence, cumulative prevalence (CP), and burden of rare hereditary diseases (RHD), comprising 72–80% of the group of rare diseases, is discussed in many reports and is an urgent problem, which is associated with the rapid progress of genetic technology, the identification of thousands of genes, and the resulting problems in society. This work provides an epidemiological analysis of the groups of the most common RHDs (autosomal dominant, autosomal recessive, and X-linked) and their point prevalence (PP) and describes the structure of RHD diversity by medical areas in 14 spatially remote populations of the European part of Russia. The total size of the examined population is about 4 million. A total of 554 clinical forms of RHDs in 10,265 patients were diagnosed. The CP for all RHDs per sample examined was 277.21/100,000 (1:361 people). It is worth noting that now is the time for characterizing the accumulated data on the point prevalence of RHDs, which will help to systematize our knowledge and allow us to develop a strategy of care for patients with RHDs. However, it is necessary to address the issues of changing current medical classifications and coding systems for nosological forms of RHDs, which have not kept pace with genetic advances.