The first step in pest control fo any organic gardener should be the soil the plants grow in. Get that into good condition so the soil will grow strong and healthy plants and there will be fewer insect pests bothering those plants. Intercropping, planting a variety of plants together, can be another good way to keep insect pests away. For the others, the animals, the best defense is a good, tight fence. Each of my planting beds is surrounded by a fence and that keeps all but the voles, chipmunks, and baby rabbits, from gaining entry. The 4 x 4 planting beds have the fence stapled to a frame that allows me to just flop it to one side when I work there, but some other planting beds (longer but not wider) have a fence all around that needs to be opened up for my entry.
That is kind of a pain, but allows me to have uneaten fruits and veggies and flowers.

Don't ask me about the furry animals, but the pests in my vegetable garden last year were turned away by plain old white baking flour. My 3rd grade daughter sprinkled it on a cabbage she was growing for a school project and the bugs left it alone. I tried it on my tomatoes, too. I didn't have to use it on my flowers and would be more hesitant to if the white powder made the blooms look bad, but to save the plant I would do it.
My daughter also got rid of black ants. She took a bottle of tobasco sauce and poured it down every hole she could find. They relocated out of our neighborhood. Think of the stories those ants are telling their children!
Beware of any remedy that includes vinegar.. While it's not a chemical, it's often acidic enough to eat through the leaves and destroys foliage.
If your soil needs help there are natural recipes. Mine isn't on this computer or I'd include it. One I read included a can of regular Coke, a can of beer, saltpeter, and a few more items I found strange. I sprayed it on and it did wonders.
If you have areas you want NOTHING to grow, instead of Roundup or some chemical use a heavy dose of salt. Of course, as with Roundup, be careful where you put it.
In the "olden days" (I've heard) dish soap used to have phosphate in it and if sprayed on the lawn would kill the worms that wrecked the smooth grass. In the spring if there are areas you don't want anything to grow in try the salt and/or cornmeal. The cornmeal has to be worked into the ground, but it prevents seeds from germinating. Don't put it with all your seeds or your flowers won't come up, either because it stops ALL germination. I haven't figured out how to work it into the soil in an effective way, but I'm thinking about it.

I rarely use anything to deal with insects. Insects are drawn to sickly plants and rapidly growing young plants. Cover young plants after planting correctly. Get rid of sickly plants or trim infected parts. I look at my plants every day and deal with the pests I find---either hand pick or drop in soapy water.

I fence for larger animals but I don't have tunneling animals so I can't help with them. I don't feed the birds.....it makes them lazy and attracts squirrels and other rodents.

Good luck and keep notes for next year.

Suggesting, on an Organic Gardening forum, that soneone use a glysophate product cast strong doubt about anything else one posts, and most of what I saw in xiangirl's post is more myth thanb reality.
Tobasco sauce will cause many insects to move, but there is no good reason to use it on ants which are, contrary to what most have been taught all their lives, for the most part beneficial.
The vinegar you buy in the store is only 3 to 5 percent acetic acid, hardly strong enough foliage damage to be of concern unless one sprayed that foliage during the heat of the day, in full sun, and wet the foliage really well. Vinegar, Acetic Acid, is a chemical.
The colas have been used also as insect repellants, as well as rust and tar removers. sometimes they work and sometimes they don't. They are very inconsistant and not worth spending your money on.
In the "old days" soaps were made by reacting animal fats with lye (produce by running water through wood ash) and it was the fatty acids in that soap the killed the insects, not phosphorus.
Corn meal is not a pre emergent, although Corn Gluten Meal is. Different stuff and the Corn Gluten Meal must be left on the surface of the soil, not worked in, to be effective. Many people here have reported using corn meal as a fungicide, but not as a pre emergent.
There have been several articles in the past year about creating a wild flower garden to aid in attracting beneficial insects that can aid in controlling the pests in your garden, you need to provide food, shelter, and moisture for a population of these beneficial insects to hang around. Companion planting is another weapon to use. Some plants are planted to attract the pests, naturtiums, while others are repellants.

The best overall insect repellant one can use is to create a biodiverse garden and follow organic principles with regards to improving soil conditions and avoiding synthetic fertilizers and pesticides. These efforts will encourage the presence of both beneficial insects and birds (nature's best insect control!) as well as reduce the potential for damaging insects.

Just because a product is considered "natural" or organic does not mean that it is not a chemical. Chemical compounds comprise virtually every naturally occurring item I can think of - some are pretty benign and others, like acetic acid or nicotine, can be extremely caustic or dangerous to use. And they may also be toxic to non-target organisms (i.e. the 'beneficial' insects) as well as the bad guys.

Why anyone would want to kill off worms is a bit beyond me. This is just another indication of the lack of understanding of the natural order and the biology of the soil in favor of a "pretty" looking lawn, a non-natural monoculture and typically a huge environmental black hole.

"instead of Roundup or some chemical use a heavy dose of salt. Of course, as with Roundup, be careful where you put it."
xiangirl, by "instead" you mean in place of, right?
My Father, a natural gardener not a organic gardener, told me the same thing.
He never used Roundup or some chemical, but instead he used salt or children. He seem to think 6 children from the age 7-14 could work for their dinner, by pulling weeds.:-)

I don't want to kill worms. I know they're beneficial. But they may be the culprit in eating carrot seedlings. At least that's one theory around here.

If you have areas you want NOTHING to grow, instead of Roundup or some chemical use a heavy dose of salt. Of course, as with Roundup, be careful where you put it.

Yes ... permanently poison the soil!

And when the salt migrates with rainwater and runoff ... then what?

"I don't want to kill worms. I know they're beneficial. But they may be the culprit in eating carrot seedlings. At least that's one theory around here."
Which "worms" are you referring to? Earthworms will not eat carrot seedlings while wireworms may be the real problem.