Here's the thing with antioxidants: yes, in the lab they neutralize free radicals and the harm they cause. You can watch it happen under a microscope or when you sprinkle your apple slices in lemon juice to stop them from turing brown.
In your body, however? Evidence says they don't do a single darn thing. In fact, one study showed that smokers who attempted to antioxidize their way out of cancer were more likely to get cancer and heart disease. Other studies have shown that oxidation (a very common instance of free radicals gone wild) can actually help wound healing and prevent aging in young folks.
Not to say you shouldn't eat those fruits and veggies, just don't pay extra for something with açai berries or whatever in it. Don't let the evil marketers win!