Nontoxic naturally occurring compounds, especially those from dietary sources, are receiving increasing consideration for prevention and treatment of diseases including cancer. There is a growing need for innovative anticancer therapies and therefore search for natural compounds with novel biological activities or antineoplastic potential is currently an important area in drug discovery. Support for this interest also comes from increasing concern over the efficacy and safety of many conventional therapies, especially those that run over a long course of time. Laboratory studies in different in vitro and in vivo systems have shown that many natural compounds possess the capacity to regulate response to oxidative stress and DNA damage, suppress angiogenesis, inhibit cell proliferation and induce autophagy and apoptosis. This review discusses the induction of apoptosis and autophagy as a mechanism of cancer prevention by some of the most studied naturally occurring dietary compounds.