Methanolic extracts of 10 selected Nigerian medicinal plants-Psidium guajava, Alstonia boonei, Cassia alata, Newbouldia laevis, Spondias mombin, Globimetula cupulatum, Chromolaena odorata, Securidaca longepedunculata, Ocimum gratissimum, and Morinda lucida-widely used in ethnomedicine, were assessed for phytochemical constituents and antioxidant and free radical scavenging activities using seven different antioxidant assay methods. Phytochemical screening gave positive tests for steroids, terpenoids, and cardiac glycosides, alkaloids, saponins, tannins, and flavonoids contained in the extracts. P. guajava contained the highest amount of total phenolics ($380.08{pm}4.40;mg/L$ gallic acid equivalents), and th highest amounts of total flavonoids were found in the leaf extracts of C. alata ($275.16{pm}1.62;{mu}g/mL$ quercetin equivalent [QE]), C. odorata ($272.12{pm}2.32;{mu}g/mL$ QE), and P. guajava ($269.72{pm}2.78;{mu}g/mL$ QE). Percentage 2,2-diphenyl-picrylhydrazyl (DPPH) radical scavenging activity was highest in S. mombin ($88.58{pm}3.04%$) and P. guajava ($82.79{pm}2.84$ and compared with values obtained for ascorbic acid and gallic acid. All the extracts, generally, had low nitric oxide radical scavenging activities, and G. cupulatum had the highest hydroxyl radical scavenging activity ($63.84{pm}0.97%$). The extracts I general demonstrated high lipid peroxidation inhibitory activity, with only M. lucida ($38.74{pm}1.99%$) and A. boone ($47.16{pm}0.59%$) being exceptions. The reductive potential was highest in P. guajava ($0.79{pm}0.04$) and least in S. longepeduncula ($0.26{pm}0.00$). DPPH assay correlated well with total phenolic contents ($r^2$=0.76) and reductive potentia ($r^2$=0.81) and fairly with lipid peroxidation inhibitory activity ($r^2$=0.51). There was a good correlation between total phenolic contents and reductive potential ($r^2$=0.79) and a fair correlation between total phenolic contents and lipid peroxidation inhibitory activity ($r^2$=0.55). These results suggest that the methanolic extracts of the studied plant parts possess significant antioxidant and radical scavenging activities that may be due to the phytochemical content of the plants and as such make them potential candidates as natural chemoprophylactic agents. In addition, multiple assay methods should be used in comparing antioxidant capacities of samples to have a reliable result.