We have assembled a large sample of virialized systems, comprising 66 galaxy clusters, groups and elliptical galaxies with high-quality X-ray data. To each system we have fitted analytical profiles describing the gas density and temperature variation with radius, corrected for the effects of central gas cooling. We present an analysis of the scaling properties of these systems and focus in this paper on the gas distribution and M-T-X relation. In addition to clusters and groups, our sample includes two early-type galaxies, carefully selected to avoid contamination from group or cluster X-ray emission. We compare the properties of these objects with those of more massive systems and find evidence for a systematic difference between galaxy-sized haloes and groups of a similar temperature. We derive a mean logarithmic slope of the M-T-X relation within R-200 of 1.84 +/- 0.06, although there is some evidence of a gradual steepening in the M-T-X relation, with decreasing mass. We recover a similar slope using two additional methods of calculating the mean temperature. Repeating the analysis with the assumption of isothermality, we find the slope changes only slightly, to 1.89 +/- 0.04, but the normalization is increased by 30 per cent. Correspondingly, the mean gas fraction within R-200 changes from (0.13 +/- 0.01) h(70)(-3/2) to (0.11 +/- 0.01) h(70)(-3/2), for the isothermal case, with the smaller fractional change reflecting different behaviour between hot and cool systems. There is a strong correlation between the gas fraction within 0.3R(200) and temperature. This reflects the strong (5.8sigma) trend between the gas density slope parameter, beta, and temperature, which has been found in previous work. These findings are interpreted as evidence for self-similarity breaking from galaxy feedback processes, active galactic nuclei heating or possibly gas cooling. We discuss the implications of our results in the context of a hierarchical structure formation scenario.