A series of synthetic chalcones, flavanones, and flavones has been synthesized and evaluated for antitumor activity against the human kidney carcinoma cells TK-10, human mammary adenocarcinoma cells MCF-7 (estrogen receptor-positive), and human colon adenocarcinoma cells HT-29. The most active series is the chalcone ones with the best results against TK-10 and HT-29 cells. Fourteen out of 53 analyzed compounds resulted very active against at least two of the studied tumoral cells. Alkaline single cell gel electrophoresis, comet assay, was performed as a study of the chromosomal aberrations promoted by the compounds on normal cells. Four active and two inactive chalcones were studied in the comet assay against normal human kidney cells (HK-2). A structure-activity relationship analysis of these compounds was performed and for 4- and 3,4-disubstituted derivatives a quantitative correlation was obtained in the case of anti-HT-29 activity.