Hi Paula,

There are a good number of pests that damage tomato fruits, including insects, but insects are not always the culprit when you find holes in the fruit. If you see evidence of insect droppings or the insects themselves, then you can probably assume it's an insect, otherwise it may take more detective work to find the culprit.

It's possible that an insect isn't the culprit at all. Many birds peck at ripening fruit, and tree squirrels and ground squirrels (chipmunks) will also steal tomatoes to eat elswehere or chew on it right on the vines. You may need to use fences or netting to exclude bird or mammal pests in the garden.

Here are two very common tomato insect pests that chew on fruit-

Tomato Fruitworm- One very common pest of tomato fruits is the caterpillar of the moth Helicoverpa zea, which if you find it on corn is known as Corn Earworm, on tomatoes it's called a Tomato Fruitworm, and on cotton, it's called the Cotton Bollworm. It's the same insect but found on many different plants. You might describe these green caterpillar-type worms as smooth, not particularly hairy and the color may range from a very pale green to pink or even almost black in color-most develop darker color patterns as they mature.

Tomato Hornworms- Hornworms are also the larvae of sphinx moths and while they most commonly eat foliage and stems, they may feed on green fruits as well. Unlike the Tomato Fruitworm which bores into the fruit, hornworms feed on the surface leaving large, open scars. Hornworms are large smoothish green caterpillars with a hornlike appendage on the hind end.

Less commonly seen on tomatoes but can still create damage:

Beet Armyworm attacks both foliage and fruit, creating single or closely grouped circular or irregular holes.

Yellowstriped Armyworm feeds on both foliage and fruit. It rarely bores deeply into the fruit, but eats on the surface, causing irregular holes.

If you determine that one of the above caterpillar insects is the problem, there are some remedies you use to help control them. With Tomato Hornworms and other large caterpillars, there may only be a few on each plant, so often you can pick them off and destroy them. They can be hard to spot and create quite a bit of damage if you aren't looking for and picking them off daily. For insects that you know are there and are hard to find (or too many to pick off), you may wish to try a spray or dust insecticide. There are several products you can get at your local garden center. It's better to start with a less toxic product first and see if you can control the pest insect and keep the beneficial insects in your garden. 

A good one to try in this case contains Bacillus thuringiensis (B.t.), which is a naturally-occurring bacteria that only affects caterpillars. Bacillus thuringiensis (B.t.) is very safe and effective in controlling the targeted pests and not other beneficials like bees living in your garden. Another benefit  of B.t. products is that you won't have to wait a certain number of days before you can harvest the tomatoes to eat, just be sure to wash them well. (Always follow label directions with any pesticide, no matter how safe it is.)  

Another product that you may try is one containing the active ingredient Spinosad. Spinosad provides control for a broader spectrum of insect pests, rather than just caterpillars as with the B.t., so you could potentially use it for other pests that you may encounter in the garden. It is more expensive to buy. Another drawback is a one-day wait after spray before you can harvest. It has restrictions as to how often you can use it in a certain time period (to help reduce the possibility of insects becoming resistant) and it is also toxic to bees when it's wet- so you won't want to be spraying while the bees are active in your garden.

You may also find some garden sprays containing pyrethrins or neem oil extract at your garden center. Be sure they are labeled for use on vegetables and follow all label directions carefully.
Here is a site from Cooperative Extension in your state that you may find helpful for this and your other tomato gardening questions.
http://www.ipm.ucdavis.edu/PMG/selectnewpest.tomatoes.html