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We present a new determination of the dust content and near-ultraviolet/optical extinction curves associated with a sample of ≃ 8300 strong, W^λ2796₀ > 1 Å, Mg II absorbers, redshifts 0.4 < z < 2.2, identified in Sloan Digital Sky Survey (SDSS) spectra of quasars in the data release 6 (DR6). Taking into account the selection effects that result from dust extinction, including the reduction in the signal-to-noise ratio of an absorber appearing in a reddened quasar spectrum, we find a stronger dependence of E(B-V) on absorber W^λ2796₀ than in other published work. The dependence of the median reddening on W^λ2796₀ can be reproduced by the power-law model E(B-V) =[(8.0 ±3.0) {x} 10^–4]{x} (W₀)^(3.48±0.3) for 1.0 ≤ W₀ ≤ 5.0. Observed Mg II samples, derived from flux-limited quasar surveys, are shown to suffer from significant incompleteness at the level of 24 ± 4 per cent for absorbers with W₀> 1 Å and 34±2 per cent for absorbers with W₀> 2 Å. Direct determination of the shape of the near-ultraviolet extinction curves, using high signal-to-noise ratio composites, for absorbers as a function of E(B-V), shows evidence for systematic changes in the form of the extinction curves. At low E(B-V) ( ≲ 0.05), the extinction curve is featureless and well represented by a Small Magellanic Cloud (SMC) like extinction curve. For intermediate E(B-V)s ( ≲ 0.2), approximately a third of Mg II absorbers show evidence for a 2175 Å feature and an extinction curve similar to that of the Large Magellanic Cloud (LMC). For the small number of high E(B-V) ( ≳ 0.3) absorbers, the majority of which exhibit strong Ca IIλλ3935,3970 absorption, there is evidence for the presence of a 2175 Å feature as strong as that found in the Milky Way (MW). Near-infrared photometry for six of the systems indicates that the rest-frame optical portion of the extinction curve for these high E(B-V), and likely very high column density, systems is significantly greyer than the SMC, LMC or MW extinction curves. Application of the new results on the dust content of strong Mg II absorbers shows that dusty absorbers can account for a significant proportion, up to a factor of 2, of the observed overdensity of absorbers seen towards gamma-ray burst (GRB) sightlines, compared to sightlines towards quasars in flux-limited samples.