In a huge survey of the literature on organic food from the last 50 years, the overall message is that no difference in nutritional value is to be found between organically and conventionally grown foods.  (By the way, I hope some day those terms will be replaced by "conventional" for what is now termed organic, and "sprayed" or perhaps "chemical" for what is now called conventional.)
The only differences found was that conventionally produced crops had more nitrogen (that's good), and that organic crops had more phosphorus (an essential element for our cells). That's it!
So why do you buy organic food? I have also heard people say it's more healthful (actually, they say "healthier", but that's would be to the food), but I like to do it because it is better not to use pesticides, hormones, and antibiotics (anything else?), since those harm us, as well as other species, such as sexually challenged frogs . If no one can find any evidence that those chemicals are bad for humans to ingest, then I would be very surprised (but then again, I wouldn't be surprised to be surprised).
 Dangour, A., Dodhia, S., Hayter, A., Allen, E., Lock, K., & Uauy, R. (2009). Nutritional quality of organic foods: a systematic review American Journal of Clinical Nutrition DOI:10.3945/ajcn.2009.28041
 Pettersson, I., & Berg, C. (2007). ENVIRONMENTALLY RELEVANT CONCENTRATIONS OF ETHYNYLESTRADIOL CAUSE FEMALE-BIASED SEX RATIOS IN XENOPUS TROPICALIS AND RANA TEMPORARIA Environmental Toxicology and Chemistry, 26 (5) DOI: 10.1897/06-464R.1
Update July 30th:
It is interesting to see the diversity of the few comments below. Tom points out that the study didn't look at micronutrients, Rachel remarks that organic farmers do in fact use pesticides and herbicides that are also not good for you, and an almost mandatory anonymous conspiracy-theorist comment that this study was funded by big agro (implying it has no validity). All I could find in the paper about finding was this:
2 The funding organization had no role in the study design, data collection, analysis, interpretation, or writing of the report. The review team held 6 progress meetings with the funding organization.I have contacted the first author for a clarification.
3 Supported by the UK Food Standards Agency (PAU221).
Update july 31st:
Alan Dangour got back to me and confirmed that the UK Food Standards Agency was the only agency funding this study. That seems to put any concerns about big agro influencing the results to rest.