There are many insects that feed on vegetable gardens and a good source for identifying these insects can be found at the link below!
Some forms of natural pest control include:
Diatomaceous Earth *See Link Below*
Soapy Water
Cucumber
Mint Tea
Garlic
Nightlights
There are only a few of the ways to get rid of unwanted pests but for more natural pesticides you can visit Eartheasy which is linked below.
If the natural way of pesticides isn't working then you can always go to your local gardening center for resources such as what pesticides are safe to use on certain vegetables such as:
Ortho
Bonide
Natria
Bayer