Some variations provide a carbon-negative carbon product that is characterized by a carbon intensity less than 0 kg CO2e per metric ton of the carbon-negative carbon product, wherein the carbon-negative carbon product contains at least about 50 wt % carbon. In some embodiments, the carbon intensity is less than −500 kg CO2e per metric ton of the carbon-negative carbon product. Other variations provide a carbon-negative metal product (e.g., a steel product) that is characterized by a carbon intensity less than 0 kg CO2e per metric ton of the carbon-negative metal product, wherein the metal product contains from 50 wt % to 100 wt % of one or more metals and optionally one or more alloying elements. In some embodiments, the carbon-negative metal product is characterized by a carbon intensity less than −200 kg CO2e per metric ton of the carbon-negative metal product. The carbon-negative metal product can contain a wide variety of metals.