It is most likely called a Tomato Hornworm, and boy can they eat! They are also extremely hard to find.
How hard? Find the one in this picture:
Did you find it? Here is a closeup of one so you know what to look for:
So how do you know to look for the Tomato Hornworm?
Simple, look for these signs:
These suckers can strip a stem very quickly, so keep looking at your tomato plants for eaten stems/leaves and droppings. Controlling them early will help keep your plants healthy and keep them producing.
So how do you get rid of them?
You can treat the plants with chemicals like Sevin dust, but then the beneficial insects will also be killed. The best way is to pick them off. You can then squish them to kill them, put them in a bowl of water mixed with dish soap, or do what I do; feed them to my chickens like this:
A great book on identifying what insect or disease is affecting your plants is What’s Wrong With My Plant? (And How Do I Fix It?): A Visual Guide to Easy Diagnosis and Organic Remedies