In the Lawn...
Ants
Ants are attracted to nutritionally poor, dry soils, low in organic matter. Generally, if you increase the organic matter in your soil by top-dressing with compost, your soil will retain more moisture and the ant problem will take care of itself. You can apply sand, borax or bone meal to the mounds also. I've also found that drenching an ant hill for a few consecutive days can persuade the ants to relocate.
Chinch Bugs
Chinch bugs like lots of thatch, dry grass roots and soil low in nitrogen. Aerate in spring and summer and de-thatch in fall. If you have hordes of chinch bugs and they are killing patches of your lawn, put a capful of dishwashing soap in a sprinkling can filled with water and drench the problem area. Then lay a piece of white flannel over the problem area. The chinch bugs will cling to the flannel as they try to escape the soap. In 15 to 20 minutes, vacuum the flannel or rinse in a bucket of insecticidal soap. Sounds crazy but it works.
Sod Webworm Moths
If you notice small whitish moths darting about, you likely have sod webworms. Best action is to aerate and top-dress with endophytic grass and de-thatch in the fall. If you need more help that this, you can try introducing beneficial nematodes as a "natural" control.
White Grubs

These grubs are soft and white, with a C-shaped body. They can be from a quarter inch to 3 inches long. And they can cause patches of your lawn to turn brown and die. The best defense is a dense healthy lawn. De-thatch, aerate and keep surface moisture to a minimum by watering deeply and infrequently.
Milky Spore Disease - a naturally occurring bacterium will control white grubs for years once well established in your soil. You can also try introducing beneficial nematodes.
In the Garden... (from Mother Earth News)
Aphid - Insecticidal soap, attracting beneficial insects, horticultural oil
Armyworm - Bt (Bacillus thuringiens), handpicking, row covers
Asparagus Beetle - Poultry (chickens, banty hens, etc), neem oil, handpicking
Blister Beetle - Poultry (chickens, banty hens, etc), neem oil, handpicking
Cabbage root maggot - Crop rotation, beneficial nematodes, diatomaceous earth
Cabbageworm - Bt, handpicking, row covers
Carrot rust fly - Crop rotation, beneficial nematodes, diatomaceous earth
Colorado potato beetle - Poultry (chickens, banty hens, etc), neem oil, handpicking
Corn earworm - Bt, horticultural oil, beneficial nematodes
Cucumber beetle - Poultry (chickens, banty hens, etc), neem oil, handpicking
Cutworm - Rigid collars around seedlings, Bt, diatomaceous earth
Flea beetle - Insecticidal soap, garlic-pepper spray, row covers
Japanese beetle - Handpicking, row covers, milky spore disease
Onion root maggot - Crop rotation, beneficial nematodes, diatomaceous earth
Slugs & Slugs- Handpicking, iron phosphate slug bait, diatomaceous earth
Squash bug - Handpicking, good garden sanitation, neem oil
Squash vine borer - Crop rotation, beneficial nematodes
Stink bug - Handpicking, attracting birds, neem oil
Tomato hornworm - Bt, handpicking, row covers
Whitefly - Insecticidal soap, attracting beneficials, horticultural oil
Beneficial nematodes are nature's way of effectively controlling the larvae stage (white grubs) of the Common Chafer, European Chafer, Japanese Beetle, Asiatic Garden Beetle, Black Vine Weevil, Strawberry Root Weevil, plus May & June Beetles.
They are a safe and sensible way to reduce white grubs infestations and other pest insects while not harming your grass or beneficial insects.
How to apply: normally you just add them to water and spray onto the lawn. Follow the instructions from your supplier. A package of 50 million nematodes will cover 2500 sq. ft. or 250 sq. metres. Make sure the ground is wet before you apply the nematodes and water the lawn each day, for a couple of days after applying. I try to apply DURING a gentle rain and when rain is forecast for the next couple of days. Luckily, rain occurs quite often in our area, in the spring and fall, when nematodes work best.