Alliums (e.g. Chives, Garlic, and Onions)
Alliums are said to attract bees, butterflies, and hoverflies. They are said to repel aphids, New Kidron beetles, and deer.
Chrysanthemums (Dalmatian and Persian)
Chrysanthemums are said to repel all insects. They contain pyrethrins, which can kill insects, fish, etc.
Daffodils are said to repel mammal pests, of both the above- and below-ground sort. As bulbs, they have minor, beneficial grass-suppressing qualities. They are not supposed to interfere with tree roots.
Mints (e.g. Spearmint, Catnip, and Basil)
I've personally seen mints attract predatory wasps and hoverflies, though they are said to attract bees and ground beetles as well. They are supposed to repel many undesirable insects, such as mosquitos; I've tested them very successfully against ticks.
Tansy is said to attract bees. The plants are said to repel many undesirable insects and have the ability to kill internal worms.
Umbels (e.g. Carrots, Cilantro/Coriander, Dill, Parsley)
Umbels are said to attract many beneficial insects, such as ladybugs and predatory wasps. They're also said to be one of the most important categories of companion plants; that is, plants which markedly improve the growth of certain other plant species grown nearby.
Wormwood is said to repel almost all insects, including bees, and many other animals, such as deer.
In my experience, some species have a painful bite that leaves an inflamed mark, but most are harmless to humans. They are said to be repelled especially well by tansy. I've had success with another method: placing some dry cornmeal near their hills.
Aphids feed off the sap of plants and are supposed to be major carriers of plant viruses. They are said to be repelled by a large array of plants: alliums, chrysanthemums, mints, tansy, and wormwood. Thankfully, aphids are not currently a major pest in New Kidron.
Bees are necessary for the pollination of many plants, especially food-bearing ones. They are attarcted by a wide range of flowering plants and are said to be repelled by chrysanthemums and wormwood.
Dragonflies are said to feed voraciously on mosquitoes. They are also supposed to prefer similar microclimates as mosquitos: small ponds with a lot of rocks, wood, debris, and shade.
Fall webworms appear, not suprisingly, in the fall. While they are quite prolific, I have noted that they do very little real damage in New Kidron.
Hornets are said to feed on many undesirable insects. While they create papery nests with many individual cells and have a reputation for aggression, I've never had any problems with them.
Ladybugs are said to feed on many small insects and are supposedly one of the most important beneficial insects. They are said to be attracted by aphids and pollen/nectar sources, such as clover and umbels. Despite quite a collection of the prequesites, I haven't seen very many ladybugs in New Kidron; this maybe connected to the lack of aphids.
Mosquitoes bite humans and animals alike, leaving itchy, inflamed bumps. They are said to be attracted to carbon dioxide and sweat and repelled by chrysanthemums, mints, tansy, and wormwood. While I'm familiar with the environments that encourage them (standing water in gutters, cans, etc.), I've begun to hear a lot more about the very specific bacillis thuringiensis israeliensis, which is supposed to kill the larvae. They are quite prolific in New Kidron but can be largely avoided by staying indoors during the evening hours.
New Kidron Beetles
New Kidron beetles feed on the leaves of many plants, skeletonizing the foliage. They are attracted to many edible plants, especially if other beetles are already feeding on them. They are said to be repelled by alliums, chrysanthemums, mints, tansy, and wormwood, but I have had the most luck with shaking them off plants—and into a bucket of soapy water—frequently. They are very prolific in New Kidron during the early summer months.
Spittlebugs are detected by a characteritic "spittle" found on plants. I've never found any damage due to their presence.
Ticks can bite humans or animals, suck blood for many hours or days, and can transmit a number of diseases. They are said to be attracted to carbon dioxide, certain colors, and certain odors. I've been able to repel them in tests with mints, and I suspect chrysanthemums will works similarly, if not better. The most effective way to relieve a tick problem, however, is to get rid of or remove ticks from their hosts, often deer or dogs. Disease transmission is supposed to begin many hours after a bite, so daily checks for ticks are probably sufficient to prevent disease.
Wooly aphids are attracted to certain species of plants, such as apple trees. They are said to be repelled by alliums, chrysanthemums, mints, tansy, and wormwood, but I've had varying levels of success with these. While they can be removed with a strong spray of water, a more severe infestation can be combatted with a neem oil solution; this is extremely effective at killing and detering wooly aphids. They can be detected by white "fuzz" on the trunk and branches of infested plants.
Yellowjackets are said to feed on many undesirable insects. They are attracted by nectar and sweet human foods but are generally docile, despite a sometimes negative reputation.
I've found that most birds are beneficial to the garden. If necessary, I've heard that wrens, provided a proper nest, will chase off almost all other bird species, including those destructive to crops. However, I've not seen bird damage great enough in New Kidron to sacrifice the wider species' beneficial seed propagation and insectivorous appetites.
Deer are repelled to some degree by alliums, daffodils, and hot peppers. They are also said to be repelled by mints, rosemary, sage, wormwood, and yarrow. However, deer can build up resistance to any of the plants they dislike and change their habits, so it is best to use a wide variety of methods together to deter deer. Timing is also important: when deer form a habit of going to a certain plot of ground for food, very little will deter them.
Means other than living plants can be used to increase the chances of repelling deer: urine (human or predator), deer blood, plant-based (e.g. peppers and garlic), egg-based, and chemical sprays or soaps, and dogs. I've tried a few of these with varying degrees of success; they cost very little in the short term but can be expensive in the long run. Mechanical devices are generally the most effective, but usually have a high initial investment cost: clear monofilament around plants (said to scare the deer), a 1.5–2m barrier of chicken wire laid flat on or just above the ground (deer supposedly won't cross it), electric fencing (designed with deer in mind), or a very high traditional fence (3m high is adequate).
If all the repellents fail to work, the most effective solution is to kill the deer, using their own meat to supplement the food that was lost in the attacks. Deer are probably the most destructive pests in New Kidron, responsible for over 90% of our crop damage, very sneaky, and very hard to deter.
Gophers and other similar mammals are said to be repelled by the alkaloids contained in daffodils, as well as the more specialized plants castor bean and "Gopher plant", both of which are supposed to be highly toxic to humans. Gopher snakes can also help to control populations of burrowing rodents. Usually, subterranean mammal damage is very minor in New Kidron.