Eight selected wild vegetables from Nepal (Alternanthera sessilis, Basella alba, Cassia tora, Digera muricata, Ipomoea aquatica, Leucas cephalotes, Portulaca oleracea and Solanum nigrum) were investigated for their antioxidative potential using 2,2-dyphenyl-1-picrylhydrazyl (DPPH) scavenging, hydrogen peroxide (H2O2), ferric reducing antioxidant power (FRAP), and ferric thiocyanate (FTC) methods. Among the selected plant extracts C. tora displayed the highest DPPH radical scavenging activity with an IC50 value 9.898 μg/mL, whereas A. sessilis had the maximum H2O2 scavenging activity with an IC50 value 16.25 μg/mL—very close to that of ascorbic acid (16.26 μg/mL). C. tora showed the highest absorbance in the FRAP assay and the lowest lipid peroxidation in the FTC assay. A methanol extract of A. sessilis resulted in the greatest phenolic content (292.65 ± 0.42 mg gallic acid equivalent (GAE)/g) measured by the Folin–Ciocalteu reagent method, while the smallest content was recorded for B. alba (72.66 ± 0.46 GAE/g). The greatest flavonoid content was observed with extracts of P. oleracea (39.38 ± 0.57 mg quercetin equivalents (QE)/g) as measured by an aluminium chloride colorimetric method, while the least was recorded for I. aquatica (6.61 ± 0.42 QE/g). There was a strong correlation between antioxidant activity with total phenolic (DPPH, R2 = 0.75; H2O2, R2 = 0.71) and total flavonoid content (DPPH, R2 = 0.84; H2O2, R2 = 0.66). This study demonstrates that these wild edible leafy plants could be a potential source of natural antioxidants.