Here are a few of the critters that commonly plague our gardens.
Borers kill black locust, ash, mountain ash, white-barked birch and stone fruit trees such as peach. Scale insects are also destructive. Both are mainly controlled with systemic poisons, obviously inappropriate for fruit trees. Scale insects can be smothered by oil-based sprays, but borers cannot.
Box-elder bugs gather in hordes in the spring on south sides of buildings and fences. They suck nutrients from box elder and maple trees but do little damage to them. You can vacuum them and empty the bag into hot soapy water or spray them with insecticidal soap.
Earwigs are startling and annoying, and although they're partly beneficial, feeding on aphids and even flies, they're also destructive, chewing on plants and jumping out of flowers into gardeners' sinks. Trap them in corrugations of cardboard and shake them into a bucket of hot soapy water each morning.
Aphids are another spring pest, which may reproduce rapidly until stems of plants are thickly covered. The worst thing about aphids is that they can and do transmit diseases. Some folks plant chives among roses to repel aphids, others blast them off with a jet of water from the hose. Most aphids cannot fly and die before walking back onto a plant. Wasps devour them, and then the other beneficial insects such as lacewing and lady beetle larvae arrive to feast on aphids.
Cabbage loopers, the green larvae of small white butterflies, dine on broccoli and other cole crops. You can keep the butterflies from laying eggs by covering the plants with agricultural fleece; organically approved sprays containing Bacillus thuringiensis kill the larvae but not other insects.
Slugs are a major pest especially of foliage plants such as hosta, acanthus and, yes, lettuce. Iron phosphate baits are effective and allegedly pet safe. Diatomaceous earth kills them but has to be reapplied after watering. Slugs feed at night, when they can be hand-picked or sprayed with a mixture of half household ammonia and half water.