There are many things to do with extra tomatoes without having to can them. Most of the solutions will take some extra work on your part, but you will be glad that you made the effort to do it when it's time to reap the benefits.
* Make salsa to freeze. Make it as mild or hot as your family will enjoy. In addition to the tomatoes, you will need onions, hot peppers, garlic, and spices of your choice. This works better with a Roma or other type of Italian tomato for a thicker sauce.
* Make a large batch of chili (or more!) and freeze in family-sized or individual meal containers.
* Turn a lot of your extra tomatoes into spaghetti sauce. Use your favorite recipe for sauce and again, freeze the sauce for future use.
* Experiment with homemade ketchup if you don't already make it. It may be fun to see how it turns out. Start with a small amount, though, in case it doesn't turn out to be a favorite.
* Homemade soup such as vegetable soup often has a crushed tomato base. This would give you a chance to use some other extra garden produce, too.
Keep in mind that plastic freezer containers will generally discolor when a tomato product is stored in them.