Aims. We present the second ROSAT all-sky survey source catalogue, hereafter referred to as the 2RXS catalogue. This is the second publicly released ROSAT catalogue of point-like sources obtained from the ROSAT all-sky survey (RASS) observations performed with the position-sensitive proportional counter (PSPC) between June 1990 and August 1991, and is an extended and revised version of the bright and faint source catalogues. Methods. We used the latest version of the RASS processing to produce overlapping X-ray images of 6.4• × 6.4• sky regions. To create a source catalogue, a likelihood-based detection algorithm was applied to these, which accounts for the variable point-spread function (PSF) across the PSPC field of view. Improvements in the background determination compared to 1RXS were also implemented. X-ray control images showing the source and background extraction regions were generated, which were visually inspected. Simulations were performed to assess the spurious source content of the 2RXS catalogue. X-ray spectra and light curves were extracted for the 2RXS sources, with spectral and variability parameters derived from these products. Results. We obtained about 135 000 X-ray detections in the 0.1−2.4 keV energy band down to a likelihood threshold of 6.5, as adopted in the 1RXS faint source catalogue. Our simulations show that the expected spurious content of the catalogue is a strong function of detection likelihood, and the full catalogue is expected to contain about 30% spurious detections. A more conservative likelihood threshold of 9, on the other hand, yields about 71 000 detections with a 5% spurious fraction. We recommend thresholds appropriate to the scientific application. X-ray images and overlaid X-ray contour lines provide an additional user product to evaluate the detections visually, and we performed our own visual inspections to flag uncertain detections. Intra-day variability in the X-ray light curves was quantified based on the normalised excess variance and a maximum amplitude variability analysis. X-ray spectral fits were performed using three basic models, a power law, a thermal plasma emission model, and black-body emission. Thirty-two large extended regions with diffuse emission and embedded point sources were identified and excluded from the present analysis. Conclusions. The 2RXS catalogue provides the deepest and cleanest X-ray all-sky survey catalogue in advance of eROSITA.