Strict standards
To be certified Organic in the United States, operations must adhere to the standards of the USDA National Organic Program. These standards ensure all food products labels organic are indeed true to such claim.

Great taste: 
Although only an opinion, it is an opinion shared by many throughout the world – many people prefer organic food because it tastes better.

No pesticides, additives, antibiotics, or other chemicals: 
Leaving these chemicals out of and off of our food makes for healthier living. For most of the chemicals put on or in our food, we aren’t even aware of the long term side effects.

Higher vitamin/mineral levels: 
Studies have shown that on average, organic food has higher levels of certain vitamins and minerals, as well as antioxidants.

Better for environment/wildlife: 
Organic agriculture protects the water supply, enriches the soil, encourages biodiversity & helps reduce the toxic burden on our bodies and our planet. It employs sound cultural production practices, replaces synthetic fertilizers, chemicals and pesticides, enhances the inherent fertility and biological life to build soil, and improves water quality.

The Down to Earth website has a good article concerning several aspects of organic vs. conventional farming, including cost, health benefits, and environmental aspects.

Medicine News Today - Organic Foods in Relation to Nutrition and Health Key Facts: discusses the dangers of pesticides, food additives and genetically modified organisms and the effect of organic agriculture on essential vitamins and minerals, antioxidants and fatty acids.

Eating Better Than Organic: a great article from time.com discussing the benefits of not just organic, but local (and especially local organic) foods also.

Can Organic Farming Feed the World? Written and published by University of California, Berkeley, this article gives a wonderful account of how organic farming is a growing necessity if we want to support our growing population.