A blogger for Scientific American has written this amply-footnoted article debunking much of the mythology that's grown up about organics. It's an eye-opener! The author claims that the point is not to be anti-organic, but just to clear up some widespread myths.
Myth #1: Organic farmers don't use pesticides. Most do, in fact, use pesticides: they just are only allowed to use "natural" pesticides, which may be just as nasty.
Myth #2: Organics are healthier. Conventional crops have more nitrogen while organic crops have more phosphorus and acidity, but nutrient content is identical.
Myth #3: Organics are better for the environment. I personally never believed the health claims, but I thought the environment was where the benefits were. The author grants that using fewer synthetic pesticides is a good thing, for sure. However, she argues 1) that by blasting plants with Bt and other "organic" pesticides, organic producers are still dumping nasty stuff into the environment; 2) that ignoring GMO's means we end up using more pesticides and other resources in the long run, and 3) organics are 20% less productive, yielding less per acre than conventional crops, so buying organics means voting to dedicated more land to agriculture instead of leaving it wild.
Myth #4: It's all or none. She notes that both organic and conventional farmers have positives, and that open-minded environmentalists will work toward improving both.
For a (non-specific) response, I went over to nutritionists Marion Nestle's web page, where she has a FAQ that addresses the issue. She says only that her personal investigations conclude that the USDA Organic label is a good thing to look for. "When you choose organics, you are voting with your fork for a planet with fewer pesticides, richer soil, and cleaner water supplies—all better in the long run." I think the author of the first piece would agree for the most part, but more information is definitely useful.
