We characterised the oxygen abundance radial distribution of a sample of 102 spiral galaxies observed with VLT/MUSE using the O3N2 calibrator. The high spatial resolution of the data allowed us to detect 14345 H II regions with the same image quality as with photometric data, avoiding any dilution effect. We developed a new methodology to automatically fit the abundance radial profiles, finding that 55 galaxies of the sample exhibit a single negative gradient. The remaining 47 galaxies also display, as well as this negative trend, either an inner drop in the abundances (21), an outer flattening (10), or both (16), which suggests that these features are a common property of disc galaxies. The presence and depth of the inner drop depends on the stellar mass of the galaxies with the most massive systems presenting the deepest abundance drops, while there is no such dependence in the case of the outer flattening. We find that the inner drop appears always around 0.5 re, while the position of the outer flattening varies over a wide range of galactocentric distances. Regarding the main negative gradient, we find a characteristic slope in the sample of αO/H =-0.10 ± 0.03 dex /re. This slope is independent of the presence of bars and the density of the environment. However, when inner drops or outer flattenings are detected, slightly steeper gradients are observed. This suggests that radial motions might play an important role in shaping the abundance profiles. We define a new normalisation scale ("the abundance scale length", rO/H) for the radial profiles based on the characteristic abundance gradient, with which all the galaxies show a similar position for the inner drop ( 0.5 rO/H) and the outer flattening ( 1.5 rO/H). Finally, we find no significant dependence of the dispersion around the negative gradient with any property of the galaxies, with values compatible with the uncertainties associated with the derivation of the abundances.