Ulysses was launched in October 1990, and its Solar X-ray/Cosmic Gamma-Ray Burst Experiment (GRB) has provided more than 13 years of uninterrupted observations of solar X-ray flare activity. Due to the large variation of the relative solar latitude and longitude of the spacecraft orbit with respect to the Earth, the perspective of the GRB instrument often differed significantly from that of X-ray instruments on Earth-orbiting satellites. During extended periods the GRB experiment made direct observations of flares on the hidden face of the Sun, providing a unique record of events not visible to other instruments. The small detector area of GRB and its optimization for very high counting rates minimized the effects of pulse pile-up. We interpret the spectra, time histories, and occurrence distribution patterns of GRB data in terms of “thermal feed-through”, the confusion of thermal soft X-rays and non-thermal hard X-rays. This effect is a systematic problem for scintillation-counter spectrometers observing the solar hard X-ray spectrum. This paper provides a definitive catalog of the Ulysses X-ray flare observations and discusses various features of this unique database. For the equivalent GOES range X2 – X25, we find a power-law fit for the (differential) occurrence frequency at >25 keV with slope −1.61±0.04, with no evidence for a downturn at the highest event magnitudes (for the relatively small sample of such events available in this study). If the nine most intense events are excluded because of concerns about the effects of pulse pile-up, the slope steepens to −1.75±0.08.