Saving our own seed for sowing over the following years is probably done by most of us for economy, convenience or security. I guess most of us save seed for the latter, for security; of favourite varieties, in case we may not be able to replace them otherwise. If you have heirloom, expensive or rare varieties then saving seed is a real necessity. It is obviously little effort to save back a portion of seeds of those crops grown for their seeds, such as peas, especially if these are large heavy seeds expensive to buy. Likewise a portion of a green manure or a herb can be selected to flower and set seed or a carrot or two can be left to set seed for not much extra work. However with any other than a truly scarce variety is the effort worth it as for many crops one bought in packet of seed contains more than enough for several years if kept cool and dry.
There are some strong points in favour of bought in seeds such as freedom from diseases. All commercial seed is rigorously checked because there is a danger that some nematode, virus, fungi or bacterial disease may just manage to sneak by on the seed. (or even more likely on a brought in plant). This danger is much greater if anything is ever accepted from other gardeners! Even your own seed may have become contaminated during growth and harvest. Also you know for sure that bought in seed will come true to type.
On the other hand when you save your own seed there is the possibility of acclimatisation or local selection; an improvement accidentally made. This occurs mostly when you sow very large numbers of seeds; the most favoured or well suited ones surviving and doing better, and these plants, naturally selected by their dominance, then make the bulk of the seed as a whole better suited to your conditions than the original bought in mix. Or we can deliberately select and speedup the process.
On the minus side of this same effect is the problem of variability; we presumably save seed with the hope of getting crops similar to our current productions and are not generally looking for any variation. This means that the modern F1 varieties can not give us useful seed as they almost always yield mixed results and not more of the same. This means we are obliged to save seed only from older, non F!, varieties -though if randomly variable offspring were no problem then this wouldn't matter much such as where we are after an improved strain.
An excellent demonstration to me of this law of genetic variation was some Globe Artichokes. These come true when propagated by offsets but are commonly sold as seed. I sowed a batch of Green Globe seed and got the usual batch of similar offspring. However one was very different; seedling variation had produced a plant furnished with the spikiest weapons of any herbaceous specimen I've ever seen. The whole plant is protected by long sharp hard thorns making the spiky heads almost unpickable. (These heads taste very good, sort of chicken flavoured, but need handling with extreme care. Mind you if I ever get an allotment again this is the ideal plant -it needs little regular maintenance, recovers well if vandalised and difficult to rob by day it's downright dangerous by night.)
Unfortunately, even without being F1, many of our commonest crops can set seed but it will not be of any great use as they will not stay true and pure. In particular the brassica family are notoriously promiscuous. Although almost any brassica can be left to flower and will set viable seed where this is not done by hand in a closed environment or a long way from any other brassicas -including the closely related oil seed rape, then it will cross and hybridise freely. However with great care (i.e. fine net bags to exclude bees and only one variety flowering at a time anywhere in sight) their seed can give a large proportion of true plants. To be fair Pak-choi grown under plastic has given me excellent seed for no effort other than the harvesting and storing.
Likewise it is easy to save seed from most of the cucurbits but again unless you are very careful they are so promiscuous you will rarely get what you started with. Fortunately they do not readily cross between distant relatives so a cucumber, a watermelon and a melon may usually be grown near each other in a greenhouse without crossing, but not always. Outdoors though all the pumpkins, squashes, marrows and courgettes have a wild sort of party resulting in mongrel offspring and saving seed requires the special precautions of cutting off the petals and impregnating the females with the desired male and then keeping all other pollen off with a bag.
The root vegetables are generally easy enough to set seed and may even come true but again only if these are the only varieties in the garden or anywhere nearby -though occasionally some of them cross with wild relations as so many belong to the same family. I find carrots easy but then the seed sticks together in clumps and are hard to sow. Salsify and scorzonera come true and are well worth saving seed from but only every couple of years as so little is needed and given good conditions it will store for several.
Celery is a hard crop to grow well and few plants are needed so it's worth letting one seed and saving from this. (As celery is so prone to bolting it's a pleasure when it's only the seed you're after.) The seed not only stays fresh for years but can also be used in the kitchen to add celery flavour to savoury dishes and baked products. The turnips, Swedes, Hamburg parsley and the turnip rooted chervil need the same care as brassicas, which I find not really worth the effort except for the scarcest sorts.
Parsnips are a special case as I want so few it seems foolish buying a packet however having once let one flower and go to seed I had more than enough for decades. At more than my own height the one stem dominated the garden and made enough seed for a field of parsnips. As the seed is short lived I only gathered enough for a year or two leaving the rest for the birds. Parsnips have come up in profusion every year since and now I never sow parsnips as I am forever weeding them out.
Beetroot can get a bit huge for a small bed and their flowering spike is mawkishly scented. However it is colourful and could be considered attractive. The Swiss chards also get huge when flowering and have the same form and mawkish scent. I have not found them easy to ripen and clean well so they are not worthwhile, again save for rare sorts -and they may cross with flowering sugar beet on fields. Likewise it seems too much effort for lettuces (which I find cross shamelessly). Leeks and Onions are simple. I saved my longest keeping onions to replant, flower and collect the seed but after several years still had no improvement over the bought in varieties so gave up. Their newer varieties had improved faster than mine. (Shallots, garlic, potatoes and so on are of course most easily grown from vegetative sets not true seed though they can equally well be so grown.)
Green manures are simple to save and the most valuable seed as so much seed is needed. I use different green manures to most, Limnanthes douglassi, Claytonia and Valerianella, as these are easier to remove or incorporate than the others and these also have alternative uses. (For more about my alternative green manures see KG August 2002)
Easiest of all is to save back some seed from our actual seed crops it seems profligate to buy in these where they come true. Peas and beans are so well known and so often grown from self saved seed it seems pointless mentioning them. But as these are such big seeds and as most do usually come true then it is worth restating how they are amongst the most economical of seeds to save to sow, especially if you buy by mail order. Just hang the pods and the dying haulm up in an airy place protected from damp and rodents. Shell them out when required or better pack the shelled seed in paper bags in tins. Of course these can also be used as a crop once dried only requiring soaking and thorough cooking. (See KG May 04).
I find Peas come fairly true with no precautions, Broad beans not so, French beans are supposed to come true but sometimes some of mine don't. Climbing French beans seem to come true but not the Runner beans if they have a chance. Soya beans may well come true but mine have hardly ever managed to return me as much seed as was sown in the first place!
Sweet corn is definitely a crop we grow to eat the seed but rarely do we ever save it for growing on. We are thoroughly discouraged from so doing by warnings of doom. It is expensive seed and you get very little in a packet so it is worth saving this seed where you can. As sweet corn is wind pollinated it is remarkably promiscuous, if you grow only one (old) non F1 variety such as Golden Bantam you should get mostly true seed. (Assuming no neighbours are also growing sweet corn and beware if you have maize, or worse GM maize, on farms nearby.)But if you have more than one sort anywhere within sight then at least save a cob from a plant in the middle of a block not on an edge. As to the F1s, well I have grown on open pollinated seed from F1 plants and as predicted got mixed results however the plants still grew and gave me a crop of eatable if admittedly somewhat variable cobs. So if you are really mean, broke or delight in diversity try sweet corn seed as the results will certainly be interesting.