Recently, you may have seen an article similar to this one, talking about a recent study which found that organic fruit and vegetables were not really more nutritious than standard industrial-farming-techniques crops. The organic crowd are attacking this study on several fronts, and they do have some points, but there are also some counter-points to consider.
First up, for some nutrients (such as beta carotene), it did appear that organic food might have somewhat more than the standard crops. However, it should be pointed out that in most nutrient categories, both kinds of crops were roughly the same. Given that, on the paleo diet, I'm typically eating 20 servings of fruit and vegetables a day, the small percentage difference isn't going to make much difference to me - I'm still getting more than 100% of the RDA of most minerals and vitamins. Further, the study does invalidate an oft-repeated claim that organic versions of produce contain "way more vitamins and minerals" (as I've heard claimed).
Second, the study did not consider the pesticide residues and their potential effects on human health. This is a valid criticism, but the study explicitly wasn't looking at that. Furthermore, it should be pointed out that organic produce is not pesticide-free - they simply use pesticides that someone, somewhere, has declared are "organic". You know what? Mother nature has made some pretty vicious poisons that I wouldn't want to be eating. Poison is poison, whether it comes from a lab or it's extracted from some beetle's venom. There are also standards for how much pesticide residue can be left on a piece of produce by the time it gets to market - I'm not sure that the same is true of aflatoxins.
The thing that the organic crowd never mentions is that organic crops, by their nature, generally have significantly lower yield per acre. If everyone on the planet switched to organic produce, we'd need to commit a whole lot more land to farming, which means a lot less land for parks, forests, and so on. Further, even organic crops generally use seeds which have been "tweaked" genetically, even if it is through years of selective breeding instead of a snip of some DNA in a lab. (For example, carrots shouldn't have nearly as much sugar in them as they do.)
While I'm on the topic of produce, someone was recently talking to me about irradiation of food. The way they were talking, it sounded like the entire produce section should glow in the dark! The truth, at least in Canada, is somewhat simpler. The only things that can be irradiated, according to government regulations, are certain spices, onions, and potatoes, and they must all be clearly labelled as such. (The fact is that there is no residual radiation in the foodstuffs so treated, but some people wonder how the treatment affects the nutritional content of the food, and I'm not 100% convinced this question has been answered to date.)
Ultimately, if you want to be sure of your own food supply, you need to grow it yourself, ideally using "heirloom" seeds (which allows you to use a few seeds from each year's crop to sow the following year's bounty). Next best would be your local vegetable stand (ideally where you can see the field your veggies just came from!), and your super-mega-food-mart is a distant third, whether you're buying organic or whatever's on sale. Being a locavore (eating food from within 100km of home) is the ideal, but I live in Canada - six months of the year all I'd get to eat would be snow! Well, not really, but you get the idea.
Update - this article raises a curious question - if pesticides are so bad for us, then why do farmers (who work with the stuff in much higher concentrations than most of us ever run into) have a cancer rate substantially lower than the rest of the population?