In 1893, A.W. Livingston published his masterwork, Livingston and the Tomato. As a pioneer seedsman, Livingston probably did more to develop the tomato as a commercial American crop than anyone. His book, now in print once again from Ohio State University Press, served as an encyclopedia of tomato varieties, with instructions for propagation and refinement. In the book, a contributor poses this advice to the question of "Should gardeners grow their own seeds?"
"This question is usually answered in the affirmative: the reason assigned being that one can grow better seeds than he can buy. The reason may have been a valid one once, and may still hold good in some cases, but to advise private parties to grow their own garden seeds is about as antiquated advice as to recommend farmers to weave their own cloth."
Granted, these were seedsmen, who made their living by selling seeds. We must also grant that in order to save seeds effectively, they should be isolated from other varieties which might cross pollinate. This would mean that you could only grow one variety of each vegetable in the garden.
In Utah, seedsman Joseph Ellis Johnson offered his catalog of more than a hundred seed varieties in 1864. All were grown from seed in Utah, for the Utah market. Seeds from eastern sources might not have seen success in Utah's hot arid climate and high altitude. Yet, on September 27 in that same year, Elijah Larkin (farming in Salt Lake City) wrote in his diary, "...I gathered my lettuce seed..."
If you're going to save seeds for next year, now is the time to do it. First you should ask, "Are my seeds open pollinated?" If your seeds are hybrid, then they won't grow again. If they are an heirloom variety, they should work. Second, you should ask, "Are the seeds pure?" If you grew pumpkins, summer squash and cucumbers all in the same patch, then the chances are good that they cross-pollinated, and whatever grows from your seeds next year will be a bizarre mix. We had a volunteer squash in the garden that we let grow for a while. It was a cross of yellow squash and cucumbers that turned out looking like zucchini. The flesh was woody and tough. We won't let any volunteers grow next year.
If you have open pollinated seed that you think is pure, there are different treatments for different kinds of seeds. Some seeds (like cillantro, radishes and lettuce) you can just let the plant go to seed, and then shake the seeds out of the seed heads into a paper bag. Other seeds take more involved processing. There's a great book called Seed to Seed by Suzanne Ashworth. She describes everything you would ever need to know about saving any kind of see you can imagine.
For tomatoes, cut the fruit in eighths, and then scrape the viscous seed blobs into a half-pint jar. Screw the lid on loosely, and set the jar on the kitchen counter for a couple of weeks until it grows a nasty mold on top, and the seeds fall to the bottom of the liquid. When you think it is ready, strain off the liquid, reserving the seeds. Spread the seeds out on a paper towel and let them dry thoroughly. When dry, store them in a paper envelope in a dark place until spring. Label the envelope.
So yeah, you can probably buy cheap seeds that require none of this effort. And if you are going to go to all the work of planting a garden, its best to not start with bad seeds. But if you're a little more adventurous in your gardening, you've probably come across some seeds that you can't buy in the store. These you would want to save. And its just nice to know that you do have some degree of self sufficiency in your soul, isn't it?