Garlic. About as fool-proof and reliable about making "seed" as they come.
Potatoes. As with garlic, if you can grow the crop, you have your "seed."
No fuss about hybrids, cross breeding intentional or not, etc. with the above as it's not an actual seed - you are growing clones. Unlike seed-producing crops, you need to save a significant portion of the harvest for next year's seed material. Use the BEST for seed and eat what's left to improve your stock, rather than eating the biggest and best.
"Lemon" cucumber. (but you can't grow other cucumbers or various type of squash nearby or you'll get hybrids.)
In general, "open-pollinated" varieties of seed are what you want if you are producing your own seed, and you have to raise the seed-producing stock (at least) in isolation from other varieties of the same vegetable or you get unintentional hybrids that may be good or bad, but in either case are not the plant you started with. Without getting into specific vendor recommendations, you'll notice that some vendors are very clear about what is and is not open pollinated, and have many open pollinated varieties in stock, and others don't. There is also the Seed Savers Exchange (not precisely a vendor) and sometimes you will find SSE varieties available from vendors if they have proved popular.
The very classic "easy to grow and quick" (but I don't know about seed production as I have not tried) would have to be radishes. 3-4 weeks to harvest in most cases. I wish I liked eating them better than I actually do, since they are so easy and generally reliable to grow.
You may also want to consider perennial crops, such as rhubarb, asparagus and (possibly crossing the line to "could be a weed") Jerusalem Artichoke (also marketed as Sunchokes - and in either case more palatable after they have had a good freeze.) Various berries, vines, shrubs and fruit trees also have the potential of long production from one purchase of "seed" material.
On the third hand, other than far-fetched scenarios that certain vendors (including some seed vendors, but none I'd purchase from) and political splinter groups like to promote, seed is not that big of an expense, and many hybrids have real advantages that outweigh the small cost of seed.