Harmful pesticides not only kill bad insects and pests, but also the good ones that, when kept around, tend to prey on the harmful insects. Killing everything throws off the natural balance. There are alternative methods to using pesticides, but sometimes as a final resort gardeners may wish to use a small range of insecticides if a pest gets out of control. "Organic" pesticides are still poisonous, but are considered less harmful than conventional pesticides. Spraying should always be a last choice, and never as a preventative.
Mild "Organic" Pesticides
One of the least harmful pesticides is insecticidal soap, made from the fatty acids extracted from plant material. This is effective against aphids, whitefly, red spider mite, soft scale and the rose slug. Insecticidal soap makes these pests slip off the plants rather than harming them, and is only harmful to very sensitive plants. Vegetable oils, made from agricultural crops are effective in keeping aphids, whitefly, thrips, scale and red spider mite off plants. This is safe for all plants but fuchsias, begonias, or seedlings because it can damage leaves. Pyrethrum is extracted from the flower heads of chrysanthemums and is used against aphids and can be harmful to some beneficial insects, but doesn't persist for very long.
Other "Organic" Pesticides
Bordeaux mixture is a compound containing copper and sulfur. It is effective against apple scab, peach leaf curl and potato blight but is harmful to fish, livestock, and worms because of the buildup of copper in the soil. Neem is created from the seeds of Azadirachta indica, and is used against many pests such as aphids, leafminers, beetles, thrips and whitefly, but is harmful to some beneficial insects. Sulfur is a naturally occurring mineral used as a dust on things like grapes to keep powdery mildew away as well as rose black spot. It can harm predatory mites, and should not be used on young apples or gooseberries.
A Truly Organic Method
A true organic way of protecting your garden against too many pests is to use "trap crops." These are plants that are used to tempt pests like slugs away from the plants you are growing. Young vegetables and bedding plants are an attractive new food source for slugs, so giving them alternative food like lettuce leaves to munch on can keep them away from what you grow. Placing old lettuce leaves under bricks or tiles, and then removing them (and the slugs on them) every few days will help to keep them down. French marigolds are also used in a similar way. Dr. Martin Warnes recommends in "Rodale's Illustrated Encyclopedia of Organic Gardening" that a pile of cut comfrey leaves can help to clear a bed of slugs before it is planted.