Hello Phoenix,
There are definitely two extremes of thought with respect to insecticide, the free sprayers and the no-sprayers. Many of these chemicals are long acting with potential health risks and hazards to the environment and groundwater, and they harm beneficial insects and pests indiscriminately.
That said, the use of chemicals should be considered after all other methods have been exhausted, and they should be used in exact accordance with the products' labeling, ensuring that adequate ventilation, low wind situation and skin and eye protection are provided. *Unused chemicals should be disposed of appropriately.
Malathion is extremely effective at eradicating aphids and spider mites. *Be sure not to use it in the vicinity of fish, pets or children.