Answer: Few insects will really damage tomato plants, but there are some. Most notable is the tomato hornworm, a very large caterpillar. These can be picked off by hand -- typically these are rare, maybe one worm per plant if any at all. You might also see aphids, these can be rinsed off with a spray of water from the garden hose. Cutworms may damage newly set out transplants, these can be deterred by wrapping a newspaper or cardboard collar around the stem at ground level.
In my experience the most likely animals to eat your plants would be deer, woodchucks or rabbits; these can be fenced out of the garden or repelled with the repellent sprays labeled for the appropriate animal.
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