According to "A Case for Mars", adequate protection can be achieved by simply filling sand bags and placing them over the shelter. Thus only a few inches (7-10 cm) of Mars soil would be required to provide adequate protection. A more accurate guess can be made with lunar soil, which is similar enough to Mars to give at least a first order guess. The lunar soil required to provide adequate radiation protection is 46 cm (18 inches). Mars would likely require less due to the atmosphere, which will protect it somewhat.
A bit more detail about the proposal from "A Case for Mars". The assumed Cosmic Ray radiation received is about 6 rem/year. The unsheltered radiation is assumed to be 9 rem/year. It seems like thicker shielding would be required for a truly long duration settlement, but these values are considerably below what the radiation exposure is in deep space, which Mars soil won't protect against.
And as Mark pointed out, to achieve the full protection of the Earth's atmosphere, one would need 14.7 psi/ Mars Soil Density, or about 12 feet (3.3 m) (roughly) of packed soil. Of course, one could get away with much less, say, 30% (Same as an airplane). That would give a thickness of about 4 feet( 1.2m)
Bottom line, I would go for 46 cm for "good" protection, and about 10 cm for "adequate" protection.