Jerry,
You can, in fact, save seeds from F-1 hybrid plants and grow them. The only problem is you will have no idea what the attributes of the F-2 hybrid will be. Additionally, the seeds may not even be F-2 but F-2 cross hybrids in the event that you may have grown several varieties of the same plant close enough together for them to have cross pollinated. Suppose you have F-1 hybrid Big boy tomatoes in your garden and close by you also have Cavalier VFNTA hybrid tomatoes and just to illustrate, you may also have pure strain Brandywine Red Landis valley tomatoes as well. Seeds you collect from the Big Boy may be big Boy F-2 hybrids (2nd generation Big Boy Hybrids), or Big Boy F-2 hybrid cross Cavalier F-2 Hybrids or even Big Boy F-2 cross Brandywines. Volunteer tomato plants that come up the next year in your garden may be anything. Any of these may produce a wonderful plant that could never be replicated since you have no idea of its parentage, or a perfectly horrid example of a tomato. You just don't know what you got, so it's a waste of garden space to include them in your garden.
Here is a great article on hybrid seeds:
http://aggie-horticulture.tamu.edu/Plantanswers/vegetables/seed.htmlAnd speaking specifically about tomatoes, my father, a master gardener, was a tomato aficianado and instilled in me the same love for growing these delicacies while still a child. I have spent many years growing them; in 1976 I produce 1,675 pounds of tomatoes with 30 plants. Just for the fun of it I once kept a single tomato plant growing and producing for three years, and this was while living in Champaign, Ilinois. Nowadays, the source of information I find to be the best regarding tomatoes is Dr. Carolyn Male, who often posts on Garden Web
http://forums.gardenweb.com/forums/tomato/ . I never hesitate to recommend her book: "100 Heirloom Tomatoes for the American Garden". I am certain you would enjoy it.
