When it comes to onions, avocados, sweet corn, pineapple, asparagus, cabbage and broccoli you don't need to worry much and can safely buy and consume the non-organic variety.
However, if you are going to eat an non-organic peach, apple, bell pepper, or carrot, you'd best clean it thoroughly first. This will eliminate some of the pesticide, but not all.
For these foods, the best strategy is to eat only the organic variety.
The Environmental Working Group has developed a guide to the "15 Cleanest" fruits and vegetables and the "Dirty Dozen" based on data from 87,000 tests for pesticide residues conducted between 2000 and 2007 by the U.S. Department of Agriculture and the U.S. Food and Drug Administration.
The complete lists and more information can be found in the poster, Pesticides in Produce: Clean 15, Dirty Dozen, a pdf file that you can download. Look for this file in the right-hand column on the top of this page under, "Download Free Posters."
Or, if you'd like to have this as an iPhone app, go to foodnews.org.