Some critters are worth welcoming into your garden. They will do a lot of good work for you: lady beetles will devour those nasty aphids; earthworms will till the soil; starlings will eat the grubs; bees will pollinate your crops.
Other critters may damage your plants, but it's worth the effort to find the safest way to control them: a blast of water will kill aphids; a wire forced into the stem of a squash plant will kill the squash vine borer larvae; hand pick that awful tomato hornworm; remove any plant part (or the whole plant) showing signs of disease. Try to live with a little imperfection if the crop is not really lost: powdery mildew seldom harms the zucchini crop.
Discover which key pests will likely show up on the vegetables you grow and learn to identify them. A few garden critters look alike, especially when you don't get a good, long look at them. They may be covered with dirt, flying by or scurrying away. At first glance, a bean beetle (harmful) may look similar to a lady beetle (beneficial); a yellow jacket (beneficial & nuisance) may look similar to a hover fly (beneficial); a house fly (nuisance) may look similar to the tachinid fly (beneficial).
Find the most specific, least-damaging-to-the-environment method of dealing with the pests. This will ensure your crops will be nutritious and safe to eat. If the idea of peaceful co-existence with garden critters intrigues you, there are some great resources available: