This research studies in detail the contents of phenolic compounds determined by the Folin-Ciocalteu reagent and the antioxidant activities determined by the TEAC (Trolox equivalent antioxidant capacity), DPPH (using diphenyl-p-picrylhydrazyl radical), and FRAP (ferric reducing antioxidant power) methods, and their correlations for used standards with these methods (catechine, gallic acid, caffeic acid, ferulic acid, Trolox, ascorbic acid, and ferrous sulfate) and extracts from several species of commonly consumed vegetables were studied in detail. The comparison of absolute values of absorption coefficients for used standards and for individual methods allows one to choose optimal common standards for methods to be compared. The procedures applied for the same sets of the extracts using identical calibration procedures and common standards allowed better comparison of the results obtained by the TEAC, DPPH, and FRAP methods. The values of content of phenolic substances and total antioxidant activity of the sets of samples correlate very well for all used methods. The very high values of antioxidant activity were found in intensely colored vegetables (red cabbage, red onion, etc.), and the values were very low in watery vegetables such as potato, marrow, and cucumber.