Yes, probably some kind of insect--beetle or caterpillar. Try getting down at eye level (or have your kids do it!

) and see if you can spot them. I'm blanking this morning on different kinds of beetles and things, but you'd probably be looking for a little black beetle; brown slugs (at least around here); or leaf green caterpillars.
A lot of times, if the problem isn't too bad--i.e. the plants are still healthy, bearing fruit--you can just let it go. It's the price of going organic! Otherwise, one of the best and safest ways to get rid of them is to handpick them off the plants. My sister taught her six year old daughter how to spot Japanese beetles and pick them from her veggies. Slightly worse infestations can be handled with a blast from the hose, so long as the plant is big enough to take it. If you plant things nearby that attract beneficial insects--yarrow, cilantro, and other herbs--then you can create a situation where the infestation self-regulates. I have an enormous celery plant in my garden right now (who would have thought that my celery failure last year would have yielded volunteer plants!) that I've left in because I noticed that it was attracting ladybugs.
There are leaf-eating ants, but I wouldn't think that's your issue.
Beyond these solutions, you might be getting into using organic (or other) sprays. There was a thread recently for a garlic/pepper spray that might work on insects as well as bunnies and other critters.