Many people believe they are.
Certainly, it is best to eat foods which have been minimally processed as well as foods which have as few additives as possible.
The key factor in organic foods is that they are generally raised using non-toxic methods of pest control and without chemical additives or hormones - so organic vegetables are less likely to contain pesticide residue and organic meat will have been fed on grains not enhanced with growth hormone, etcetera.
In the long run, your overall health may depend less on whether you ate organic than whether you ate sensibly, maintained a healthy weight and followed general habits for good health (limit drinking, stop smoking, and so on).