Part of creating an environment that is diverse and naturally protective against pests is to build healthy soil.  Many unseen natural pest controls exist in the soil.  Most pest insects have a larval stage where they are more vulnerable to natural pest controls and frequently that stage occurs in the soil where those unseen critters can get at them.  Also, healthy soil provides plants with the nutrients they need to be healthy and able to fend off pests.  

Birds are great natural pest controls that eat insects so creating a bird-friendly habitat can also help.  Use of toxic pesticides is a real turn-off for birds.  Better than using pesticides to eradicate the problem is, as Umbra suggests, removal of the distressed plant - at least for this year.  Work on building your soil and your environemnt and try basil again next year.  Or try planting it in pots in another part of the yard.  Or trading what you have growing well with someone else who has a good crop of basil.  

I would also go for the praying mantises and ladybugs - they do help, they are fun to watch, and they change the habitat for the better since they do start to get established if you've created good conditions for them.  They are also a strong incentive not to be tempted to use toxics cause once you have a resident population of mantises or ladybugs you won't want to spray.
Barbara

Build a healthy environment in your garden and you'll create a place where life of all sorts will want to be.

Our garden is full of life, and yes, it includes slugs, aphids, and earwigs and other critters that vendors of toxic chemicals love to portray as pests to extract millions of dollars from us that could be better spent on compost bins, bat boxes or backyard beehives. You do not need to expose yourself, your family, your neighbors, and the other equally important life forms that inhabit the planet to long-lived poisons that are unneccessary for a healthy garden.

Bugs of all sorts play an important role in achieving the type of balance that allows everything else to flourish. Do they occasionally nibble a tender shoot? Sure, but they also provide a food source for the other birds and insects that you want spending some time in your yard. Overtime, and as the balance of your yard improves (improved soil, variation in type, size, and density of plants, sources of water, places for insects to reside) you'll see a greater range of creatures taking up residence. And you'll see your garden with new eyes and find yourself thrilled that the basil has been munched, knowing that your actions have made a contribution to the health and well-being of your garden, your neighborhood, and the planet.

One of the principles of natural pest control is that you have to have pests in order to have natural pest predators. So, paradoxical as it may seem, patience is often one of the most important weapons a gardener can use against pests.
   Insect outbreaks follow a typical pattern: The population of pest insects skyrockets, which eventually attracts predators. Once the predators are assured of a reliable food supply, they breed, which produces a lot more predators. The pest outbreak then begins to subside as pest insects are gobbled up. But this process takes time. If it's disrupted (for instance, by an impatient gardener who decides to resort to pesticides), it may never happen at all.
   Sometimes predators can't keep up with an insect outbreak, of course, which is why Umbra is quite right to say that it's best to know what you're dealing with. However, it's amazing how often patience pays off. Your friendly local predators will come to the rescue--but you have to give them a chance!
   Incidentally, Umbra is also quite right to warn people off importing insects to the garden. If you provide good habitat and avoid using pesticides, most likely there are plenty of local predators, from lady beetles to wrens and other birds, that will be more than happy to control pest insects for you.

I work in the great state of Washington, and some of my job includes educating elementary schools about the fast fading prairie ecosystem. One of our projects?? Collecting those praying mantis egg cases and keeping them OUT of the prairie (they usually end up in school science labs for the kids to watch).
The Praying Mantis is an invasive species in our region, and is killing many of the bugs that are neccessary to a healthy praire. Make sure to do research, and keep them out of your region if they shouldn't be there! Invasives can do a lot of damage, especially if you are trying to restore landscapes!

I always discouraged customers at the garden center where I worked away from buying lady bugs or praying mantis eggs when I worked in a garden center, not for any environmental reasons, but mainly because they don't work very well, espeically for aphids.
Aphids, usually, will not kill the plants that they infest if they are large plants, like trees and rose bushes, although they are messy and unsightly.  Also, they produce a sugary waste that attracts bees, wasps and other creatures that sting and frighten children, which was the biggest complaints about them we got.  But, as irritating as they may be, they will most likely all die come winter and will only be a problem for one summer season.
Lady bugs and praying mantis do not work well for the main reason that there are too many of the aphids to eat.  For most of the year, each generation of aphids are born already pregnant with the next generation of female aphids, and millions of pregnant aphids are born to the mommy aphid within a few days of her birth.  It takes a ton of lady bugs and praying mantis to keep up with that.  Most lady bugs do fly away, and although a praying manis egg will hatch up to 200 little, baby mantis (which are very cute, by the way, the sort of dance), most of them eat each other and you only end up with the one or two strongest, who will proceed to fight to the death or mate if they ever run into one another, and if they mate the female will eat the male when they are done!  The best way to get rid of aphids, if you must, is to use mildly soapy water.  Spray down a tree and wipe down the leaves and branches of a smaller bush.
If you are going to release lady bugs the best time to do it is in the evening.  That way they will be more likely to land for the night and hopefully when they see how many bugs you have they will be less likely to leave in the morning, but still many of them proceed to fly off.  They do not have logic like we do.
At least, this is what the horticulturist at our garden center taught me.

I've been experimenting with companion planting. There are some good ideas in Rodale's Organic Gardening book mentioned in the article. I have tried using nasturtiums to attract all the aphids in the yard, and keep them off my other goodies. They are pretty if you don't look at them too closely, and the aphids love them so much, they tend to leave things near them alone. Who'da thunk it? Hopefully the nasturtium gods and goddesses will forgive us the sacrifice.

Correction to the article: toxics are not a last resort. They are not a choice. If it's the wrong plant in the wrong place, change the place or the plant. Period. It's too important- they don't just go away.

-liese

There is also a non-toxic, biological control for Japanese beetles called milky spore disease. It comes in a granulated form that you spread in the spring. The larval form of the beetle, called grubs (which can damage lawns from underneath), dies from the disease and thus does not reproduce. The disease is very species-specific, so it doesn't harm other beneficial insects, and can persist and spread for several years, benefiting your whole neighborhood. It is safe and nontoxic, and is the only way I've ever found to reliably protect my roses and grapevines from being reduced to lace.

Thanks, Umbra, for taking my question! And thanks to everyone for the great recommendations--I can't wait to put some of these strategies to use.

And I'm definitely going to look for the Rodale and Garrett books.

Last year was a bad year for Japanese Beetles in Colorado.  Tons of plants' leaves looked like swiss cheese.  The pretty little beetle that was the cause was on several edibles.  I looked up companion planting to keep them away in the future.  Garlic was listed.  I happened to have one of my favorite products nearby - Dr. T's Insect Repellant.  It contains Garlic Oil, Mint Oil & Lemon Oil.  Since it is an oil, I waited until evening (didn't want to fry the leaves).  When I sprayed on the repellant, the beetles ran & jumped away so quickly it was funny.  They didn't seem to like anything else nearby, so I never saw them again.