By definition, pests are something you don't want around. Pest control is about ways to repel pests and, if that doesn't work, to get rid of them or at least reduce the number.
Keeping pests out and discouraging their entry into your home is better than getting rid of pests or dealing with them once they are there.
- store wood off the ground
- seal holes into your home
- store food in pest proof containers
- some of the pests than like some garden plants don't like others -- suggestions
Keep in mind that some bugs will help control others. For instance ladybugs can be used to get rid of some harmful garden pests (including aphids, mealy bugs, leaf worms). Praying mantids are another beneficial insect. They will feed on many of the larger insect pests including grubs, beetles, leafhoppers and caterpillars. Bats eat mosquitos, but are not good in the attic. Whether something is a pest can depend on where it is and how many there are.
Getting rid of pests
There are often services you can call to remove pests. Depending on the type of pest, you may wish to use an exterminator or a live, "humane" service. Here are some things you can do yourself.
Boric acid is a useful way to get rid of cockroaches. They crawl through it and take it back to their nests where it kills them and their young. The other good thing about using boric acid is that it's not very toxic to humans and their pets. Sprinkle it on the counter ledges and edges of the floor where the cockroaches will crawl through it.
Rats and mice
Some of the ways that people use to get rid of rats and mice are to kill them with traps, especially snap traps or poison (careful of the safety of humans and pets in the home). Then there are other way that get rid of these pests by making them want to leave or avoid a place. These include live traps, ultrasonic waves and pest repellant (these last two are of controversial effectiveness). Some people say they will avoid places with peppermint essential oil (or oil of peppermint), fox urine, mothballs, Downy dryer sheets, mint plants or ammonia.
Suggested baits for traps: peanut butter, mouse food (from a pet shop), peanut butter and oatmeal, fried bacon, peanut butter m&ms, Swiss Miss hot chocolate mix.
There are multiple ways suggested to get rid of ants -- especially before they have established themselves. Try vinegar, black pepper, cayenne pepper, mint, bay or eucalyptus leaves or cinnamon. These things are not toxic for humans or pets, but some kinds of ants don't like them.
A mixture of borax and sugar is a popular suggestion. The sugar attracts the ants and the borax is taken home and eaten by the nest, killing them. Boric acid is also recommended in a similar manner. And cornmeal works in a similar way; the ants eat, but cannot digest it. 
Talcum powder, especially scented, and various other powders are also supposed to be ant repellants.
Orange oil can also be used to get rid of ants or termites.
Some plants that mosquitos are supposed to stay away from are (in order to be effective the scent must be released by crushing some leaves)
- ageratum (don't use on your skin)
- mosquito plants (apparently more than one plant has this name)
Hang clear plastic bags filled with water to keep flies away from a porch or other outside area.
Use the peel from citrus fruit to keep spiders away. Take the peel and rub down any area of the house where spiders often appear. (windowsills, bookshelves, bathrooms, etc.)
- Howto to rid your home of mice on WikiHowTo
- the Frugal Life on Getting Rid of Ants
- Professional Wildlife Removal for animal control services in the US, also their article on Rat & Mouse Control & Removal
- Weekend Gardner on Homemade Marigold Calendula Spray: Organically repels chewing and leaf cutting insects -- repels leaf cutting and chewing insects like: leaf cutting bees on your roses and lilacs, asparagus beetles, tomato hornworms.
- Capital District Community Gardens on how to Recognize Insect Pests & Use Organic Pest Control, including Companion Planting
- Controlling Ants in the House from the Geeky Housewife blog
- Getting rid of mice on the Gardenweb
- Pest Library - Help to Identify Household Pests