In this paper, we compute rest-frame extinctions for the afterglows of a sample of Swift gamma-ray bursts (GRBs) complete in redshift. The selection criteria of the sample are based on observational high-energy parameters of the prompt emission and therefore our sample should not be biased against dusty sight-lines. It is therefore expected that our inferences hold for the general population of GRBs. Our main result is that the optical/near-infrared extinction of GRB afterglows in our sample does not follow a single distribution. 87 per cent of the events are absorbed by less than 2 mag, and 50 per cent suffer from less than 0.3-0.4 mag extinction. The remaining 13 per cent of the afterglows are highly absorbed. The true percentage of GRB afterglows showing high absorption could be even higher since a fair fraction of the events without reliable redshift measurement are probably part of this class. These events may be due to highly dusty molecular clouds/star-forming regions associated with the GRB progenitor or along the afterglow line of sight, and/or due to massive dusty host galaxies. No clear evolution in the dust extinction properties is evident within the redshift range of our sample, although the largest extinctions are at z ∼ 1.5-2, close to the expected peak of the star formation rate. Those events classified as dark are characterized, on average, by a higher extinction than typical events in the sample. A correlation between optical/near-infrared extinction and hydrogen-equivalent column density based on X-ray studies is shown, although the observed N H appears to be well in excess compared to those observed in the Local Group. Dust extinction does not seem to correlate with GRB energetics or luminosity.