Low-resolution optical spectroscopy and visual, UBVRI and high-speed photometry of WX Cet during its 1989 June outburst are presented. The photometry showed that the outburst lasted at least three weeks. Superhumps with a period of approximately 80 min were discovered from high-speed photometry obtained during six successive days, although aliasing ambiguities prevented a precise determination of the superhump period. Nevertheless, this constrains the orbital period of WX Cet to be slightly less than approximately 80 min. The spectra showed broad, shallow Balmer absorption lines superimposed on a blue continuum. Evidence was found for gamma-velocity variations from day to day, similar to the spectroscopic behaviour of some SU UMa stars during superoutburst. Orbital periods for WX Cet and other WZ Sge stars suggested in the literature are discussed and, in many cases, shown to be very unreliable. A list of possible, probable and certain WZ Sge stars is given along with some of their salient properties. From consideration of the defining properties of the WZ Sge and SU UMa subclasses of dwarf novae, it is concluded that there is no reason to retain the distinction between these groups. The implications of the long quiescent intervals between the outbursts of the WX Cet stars are briefly discussed for the disc instability and mass-transfer instability models of dwarf nova outbursts.