There are ways to deal with pests in your garden without turning to pesticides.

There is a set of 6 steps for Integrated Pest Management:

Step 1 - Prevention

Keeping your plants healthy will prevent them from becoming infected with disease or pests.  Things like fertilizing, aerating, and mowing will create strong grass and will supress the weed growth.  Fertilizing and proper pruning will allow your shrubs & trees to be healthy and less likely to attract pests.  Try selecting more disease resistant plants & cultivars.

Step 2 - Identification

Identifying the pest correctly allows you to treat it accordingly and successfully.

Step 3 - Monitoring

Keep an eye on the damage that is being done.

Step 4 - Action Levels

Even if a pest is present it may not be causing a problem but being beneficial.  Some pests attract beneficial organisms to your garden. 

Step 5 - Treatment

Physical Treatments include mulching, pulling off infected leaves, and pulling weeds.

Cultural Treatments include planting resistant varieties and insuring your irrigation methods and timing are correct.

Chemical Treatments include using naturally derived pesticides, such as insecticidal soaps, insect pheromones, etc.

Step 6 - Evaluation

Did your treatment method work?  Learn from the experience and what could be done differently next time.