Chemical free gardening is healthier for gardeners, consumers, and the environment. Chemicals from farm and lawn runoff in Florida have been linked to red tide, which not only kills sealife, but causes respiratory problems in humans and animals. Lawn and garden chemicals leach into our groundwater, and are still present in municipal water supplies, even after processing. It is unclear what the long term effects of these chemicals is on human health, but in recent years many disorders such as infertility, ADHD, Bipolar Disorder, and Autism have become more and more prevalent in industrialized societies where chemicals are most used.
I've written two articles on natural pest control that will educate you on what is available, and how to use it.
Very basic information can be found here:
Organic Gardening Basics: Natural Insect and Animal Pest Control
More detailed information on Neem Oil, Spinosad and Homemade Pesticides can be found here:
Natural and Homemade Pesticide Alternatives for Your Organic Garden