Depends on the insects. Many can be deterred by a spray bottle of water mixed with dish soap. You can also look for insecticidal soap at garden stores. It's worked great on the aphids on my tomatoes.

Neem is pretty good for a lot of things, worth investigating.

Try looking for something at www.pharmsolutions.com. I use their "Rose Pharm" spray, which is made from peppermint oil, on my roses.

I use a mixture of DrBronner's (peppermint, but I don't know if that matters), a little olive oil, some hot sauce and a lot of water. You need to rinse the herbs before you use them, but nothing in that list is poisonous.

I have a nice recipe up on my blog that works for most stuff - it's dish soap, a small amount of alcohol (make sure you water the plant well before you do this), garlic, chili and a little lemongrass essential oil.

That said nothing gets off Japanese beetles. Baby godzillas, those little bastards.

Cover your plants under airy tulle. I haven't had a single chomp from any caterpillars on my broccoli thanks to tulle.

My husband found a recipe for boiling down like 2 cups of water with chopped up: 1 onion, a few cloves of garlic and 2 jalapeno peppers. You let it boil on the stove for a bit (Its surprisingly pungent and off-putting) strain the liquid off and put it in a spray bottle. It worked on every vegetable we grew this summer!

i 2nd the neem oil recommendation. amazon has a decent sized and priced option.