They can defoliate a plant in a hurry!
You definitely want to get rid of them as quickly as possible if they show up...
However, you don't want to douse your plants with chemical pesticides to take care of the problem. You are going to be eating those tomatoes after all...
The good news is there are usually only about 2-5 hornworms per plant when you have them. There aren't thousands of them like there might be of aphids, so it is feasible and the best option, to pick them off by hand...
The problem is that they camouflage in so well with the plants that it is dang near impossible to see them!
See if YOU can spot the hornworm in the picture below...