We present the SCUBA Legacy Catalogues, two comprehensive sets of continuum maps (and catalogs) using data at 850 and 450 mu m of the various astronomical objects obtained with the Submillimetre Common User Bolometer Array (SCUBA). The Fundamental Map Data Set contains data only where superior atmospheric opacity calibration data were available. The Extended Map Data Set contains data regardless of the quality of the opacity calibration. Each data set contains 1.2 degree x 1.2 degree maps at locations where data existed in the JCMT archive, imaged using the matrix inversion method. The Fundamental Data Set is composed of 1423 maps at 850 mu m and 1357 maps at 450 mu m. The Extended Data Set is composed of 1547 maps at 850 mu m. Neither data set includes high sensitivity, single-chop SCUBA maps of "cosmological fields" nor solar system objects. Each data set was used to determine a respective object catalogue, consisting of objects identified within the respective 850 mu m maps using an automated identification algorithm. The Fundamental and Extended Map Object Catalogues contain 5061 and 6118 objects, respectively. Objects are named based on their respective J2000.0 position of peak 850 mu m intensity. The catalogues provide for each object the respective maximum 850 mu m intensity, estimates of total 850 mu m flux and size, and tentative identifications from the SIMBAD Database. Where possible, the catalogues also provide for each object its maximum 450 mu m intensity and total 450 mu m flux and flux ratios.