A number of studies show that general antioxidant supplementation interferes with beneficial processes, and is thus harmful to long term health. This post references some of the more recent research on this topic:
You may remember a study that suggested that antioxidant supplement actually negated the effects of exercise in muscle tissue. (The reactive oxygen species generated are apparently being used by the cells as a signaling mechanism, one that you don't necessarily want to turn off). That was followed by another paper that showed that cells that should be undergoing apoptosis (programmed cell death) could be kept alive by antioxidant treatment. Some might read that and not realize what a bad idea that is - having cells that ignore apoptosis signals is believed to be a common feature in carcinogenesis, and it's not something that you want to promote lightly.
Here are two recent publications that back up these conclusions. The BBC reports on this paper from the Journal of Physiology. It looks like a well-run trial demonstrating that antioxidant therapy (Vitamin C and Vitamin E) does indeed keep muscles from showing adaptation to endurance training. The vitamin-supplemented group reached the same performance levels as the placebo group over the 11-week program, but on a cellular level, they did not show the (beneficial) changes in mitochondria, etc.
Then there's this report in The Scientist, covering this paper in Science Translational Medicine. The title says it all: "Antioxidants Accelerate Lung Cancer Progression in Mice". In this case, it looks like reactive oxygen species should normally be activating p53, but taking antioxidants disrupts this signaling and allows early-stage tumor cells (before their p53 mutates) to grow much more quickly.
This is all rather frustrating when you consider the nonstop advertising for antioxidant supplements and foods, especially for any role in preventing cancer. It looks more and more as if high levels of extra antioxidants [at] the very least help along any cancerous cells that might arise on their own. Evidence for this has been piling up for years now from multiple sources, but if you wander through a grocery or drug store, you'd never have the faintest idea that there could be anything wrong with scarfing up all the antioxidants you possibly can.