EWG (the Environmental Working Group) has put out their annual list for which fruits and vegetables they found to have the most pesticide residue, termed the “Dirty Dozen”:

1. Strawberries
2. Apples
3. Nectarines
4. Peaches
5. Celery
6. Grapes
7. Cherries
8. Spinach
9. Tomatoes
10. Sweet bell peppers
11. Cherry tomatoes
12. Cucumbers

For the last five years apples were #1, but now it's strawberries, apples #2.  So you would most likely benefit the most from buying these items organic if you were choosing.

EWG's “Clean Fifteen” lists the fruits and vegetables that had the least pesticides in them and you can safely eat with minimal concern for pesticides:

(via "The 'Dirty Dozen' Produce Named Worst for Pesticide Exposure", ABC News)

How much pesticides are in non-organic fruits and vegetables? In 2012 tests by the FDA (U.S. Food and Drug Administration) had about 70 percent of fruits and 61 percent of vegetables grown in the U.S. with detectable levels of pesticide residues. And 98 percent of fruits and 95 percent of vegetables were below legal limits set by the EPA (U.S. Environmental Protection Agency).

How safe are non-organic fruits and vegetables? According to the ABC news article:

While some shoppers are clamoring for organic produce and avoiding pesticides, the health effects of buying organic are still unclear. Prior studies have associated pesticides with poor health outcomes like cancer in children, behavioral problems, and even lower cognitive function. But a review of prior research, published in 2012 in The Annals of Internal Medicine, found a lack of strong evidence that eating organic foods led to better health.

The American Academy of Pediatrics (AAP) refers pediatricians and parents to the EWG for information when looking to reduce pesticide exposure. However, they explicitly state that it is more important for children to eat a wide variety of produce, conventional or organic. They also encourage washing produce thoroughly.

EWG's full list, from most pesticides to least:

* A small amount of sweet corn, papaya and summer squash sold in the United States is produced from GE seedstock. Buy organic varieties of these crops if you want to avoid GE produce.