Aphids are easily dispatched with sharp streams of water to knock them off the plant. Some believe this allows them to return which they do not. What appears is the next generation that wil then need to be knocked off.
The Colorado Potato Beetle can be controlled with Bacillus Thuringiensis - tenebrionis in the early stage of life with Neem Oil products and Spinosad more potent and more broad spectrum followed on the scale of more potent and broad spectrum by pyrethrin products.
Squash bugs are somewhat more complicated but Floating Row Covers early on can help. spraying with Kaolin clay can help, Neem Oil Products can help, Spinosad can help, as can pyrethrin products. Spinosad is very toxic to bees so due care in its use is necessary.

As they feed, aphids excrete a sweet, sticky honeydew onto the leaves below. This allows a sooty mold to grow, which, in addition to being ugly to look at, blocks light from leaves. Also, some aphids spread viruses as they feed.

Spray aphids with insecticidal soap, summer oil (on tolerant plants), and homemade garlic sprays.

When overwintering adults begin to emerge, shake adults from plants onto a dropcloth in the early morning. Dump beetles into soapy water. Pick off adults and larvae. Scout for eggs on undersides of leaves and destroy.

Apply parasitic nematodes to soil to attack larvae as they prepare to pupate; apply Beauveria bassiana or spinosad to kill larvae; as a last resort, spray infested plants with neem.

Yellow summer squash are generally very attractive to squash bugs, as are buttercup squash and large pumpkins. When grown as crop plants, these attractive strains should be protected with floating row covers until they start to bloom heavily. You also can use a small planting of early yellow squash as a trap crop for squash bugs. When a number of squash bugs have gathered on the plants, place a bag over them and pull them up. Pull only one plant at a time, which forces surviving squash bugs to move to neighboring plants.

Against aphids it is possible to use water from tomato leaves. Get 1 cup of cut tomato leaves /pinch off ones from the bottom/, cut them as small as possible, and pour 2 cups of water over them. Let the mixture sit at room temperature for at least 8 hrs. After that time, drain fluid and spray plants. I got rid of aphids on my veggies and on a peach tree this way last year. With my peach tree, I dipped branches of the tree in the tomato leaf water. You will have to repeat at least once, two times a week if infestation is really bad. Good luck
Another way is to get lady bugs. They eat aphids. Good luck

Keep in mind that Insecticidal Soaps can be as toxic to beneficial insects as any other pesticide and Spinosad is highly toxic to bees.
Steeping tomato leaves in water and then spraying is as effective as a straight water sprays so messing around mixing that may not be a good use of time. All I find about tomato leaves as a pest control is anecdotal.

True, the use of tomato leaves as a pesticide is anecdotal, but it's not exactly unjustified.

Solanum lycopersicum is well known to produce saponins and terpenoids that are insecticidal, feeding deterrents, or otherwise antagonize pests. Pests that attack tomatoes obviously have evolved mechanisms to compensate, but it's very possible that pests that do not attack the Solanum family are susceptible.

There's also no question that compounds from related plants are potent insecticides.. and many are also very toxic for humans.

wow, some very informative answers here! Thank you every one!
Right now, I collected some lady bugs and put them on the tomato plants. I was amazed to watch one, as I placed it next to an aphid, jump on it and devour it! lol, I had no idea they ate greenfly until recently.
I've noticed a decrease (to maybe none) of the cucumber beetles, and I picked off all the potato beetles and disposed of them.
My nemesis now is the squash bugs. When they hatch, I've sprayed a 'tablespoon of liquid soap with full bottle of water' mixture in spray bottle, on them. It seemed to kill the little ones immediately. But they are multiplying faster than I can turn around! Could this spray be paralyzing them, so they just wake up later? I think they are killing my pumpkin plant. or perhaps the soap is?? :(

Hi! Helpful - use Diatomaceous Earth. We use it for all pests with an exoskeleton. I just had the hubs dump some on a bunch of ants, and they were gone in just a couple hours. Here is the link to where we bought it - http://www.kelp4less.com/shop/diatomaceous-earth/. It's a pretty good price there, too. :) Hope that helps!

brittiem, when someone subscribes to this forum and on the same day posts a link to a web site that sells product most of us consider that that person is selling stuff which is contrary to the usage rules of this web site, ie. spam.
Diamotaceous Earth is widely available in garden centers everywhere.

Is DE safe to spread over leaves etc, or is it something I should put on the ground only? I've heard of food grade DE too. I guess I should try that stuff? :) If it's available at Tractor Supply I can get some easily. Thanks for the idea!

Insecticidal soap has very limited liability towards beneficial insects. First it is only effective on soft bodied insects - has no impact on bees, parasitic wasps, ladybugs and their larvae, etc. And it has to come into direct contact with (ie. coat) the targeted insects to be effective. Just residue on foliage is harmless to both the target species and any beneficials.

Whatkatydid: Although DE is one of the least harmful pesticides, it's sorta broad spectrum. To apply to foliage would possibly harm the beneficials as they walk over it. Plus, I'm not sure of what danger it may have to the foliage itself. I just use it on the ground.

Yes... food grade is what you want.

Kevin

Insecticidal Soap sprayed directly on a beneficial such as a bee, Lady Beetle and its larva, etc. can be as harmful to them as it is to any other insect. Insecticidal Soaps can be used to aid in control of Japanese Beetles, if sprayed in the morning before they become active.
Diamotaceous Earth works by cutting the exoskeleton of the insect that crawls over the material so the insect then "bleeds" to death. DE then can also do harm to beneficials if not used with due care.

Thank you all! :)

"Insecticidal Soap sprayed directly on a beneficial such as a bee, Lady Beetle and its larva, etc. can be as harmful to them as it is to any other insect. Insecticidal Soaps can be used to aid in control of Japanese Beetles, if sprayed in the morning before they become active."

Sorry, but that is simply not true. Insecticidal soaps are not considered broad spectrum insecticides because they only target soft bodied insects. They have a well-established reputation for being virtually harmless to beneficial insects. They have no impact on anything with an exoskeleton.

From CO State: "Insecticidal soaps are considered selective insecticides because of their minimal adverse effects on other organisms. Lady beetles, green lacewings, pollinating bees and most other beneficial insects are not very susceptible to soap sprays."

From an organic gardening site: "The insects must come into direct contact with the spray droplets for the material to be effective. Good coverage is essential. It does not kill beneficial insects such as ladybugs, praying mantis and others. Note: Some entomologists have concerns about impact of soaps on soft-bodied immature predators, such as lady beetle and lacewing larvae. No real data has turned up that substantiates these fears, however, until such data surfaces, perhaps refraining from using soaps where there are numbers of these beneficial larvae (until they mature) would be advisable."

From WSU extension service: "Many of the beneficial insects in gardens are not harmed by soaps. Bees, wasps and adult beetles are not affected. Sometimes, however, the larval stage of beneficial insects may be killed."

And from Clemson University: " Insecticidal soaps have many advantages when compared to other insecticides. They are inexpensive to use, are among the safest pesticides, leave no harsh residue, are natural products that are virtually non-toxic to animals and birds, and can be used on vegetables up to harvest. Most beneficial insects are not harmed by soap sprays."