SU UMa stars are characterized by 'superoutbursts', which are brighter at maximum light and which last much longer than the more frequent 'ordinary' outbursts of these dwarf novae. Although there are now more than 1180 SU UMa-type dwarf novae catalogued, our knowledge on their superoutburst cycle length C_so_ has hitherto been limited to about 6 per cent of the entire sample of known SU UMa stars. Using public data bases we have determined new C_so_ values for a total of 206 additional SU UMa stars in the range 17d<C_so_<4590d (including some ER UMa and WZ Sge-type representants) within total time intervals between 2 and 57yr, and with an estimated uncertainty of +/-11 per cent. This way, we are increasing our present knowledge of C_so_ values by a factor of ~3.8. Their distribution is characterized by a broad maximum around C_so_~270d, and slowly decreasing numbers up to C_so_~800d. The domain C_so_>450d was unexplored until now; we add here 106 cases (~51 per cent of our total sample) in this range of long cycles, implying a better statistical basis for future studies of their distribution. Our sample contains 16 known WZ Sge stars, and we propose WZ Sge membership for five others hitherto classified as ordinary SU UMa stars. Individual superoutburst timings deviate on average by about +/-7 per cent of the cycle length from their overall linear ephemeris, confirming the pronounced quasi-periodic repeatability of superoutbursts. All relevant parameters are listed with their errors, and a table with individual superoutburst epochs of our targets is given, enabling future researchers to combine our results with other (past or future) observations.