The row of asparagus at the back was started from seed from a population that was somewhere else on the property originally. Isn't it gorgeous? BTW: This is a picture from our new property (assuming nothing goes awry). Notice the field of squash in front of it. That's a lot of plants. Oh and please ignore the corn chip bag. In my defence, I was in a hurry and we had to spend the day there doing inspections so my kids ate chips okay!
When saving seeds, it is almost always better to take a few seeds from lots of different plants, preferably from different populations, then a whole lot of seed from just one plant. In this way, you increase your chances of having a diverse genetic population which will help your plants adapt to your growing conditions and the various curve balls sent from nature like insect plagues, disease and adverse weather.
If collecting from wild populations, be aware of whether the plant is rare or protected. If it is dirt common - like dandelions - then there is probably no harm in collecting lots but if it is rare then you may want to skip the seed collection or take a very few and give extra care to those plants. Afterall, you will be protecting a rare species. There may be rules against any sort of collection on protected plants.
Breaking the rules on purpose
Sometimes, you'll have a plant that is very different from its neighbours and you may want to try saving seeds from just that one to see if it will produce offspring that display its special characteristics. Other times, it may just be one part of the plant that has different fruit, flower colour, leaf shape etc... Assuming that there is no pathological cause, it might be a sport. This may mean that, that particular part of the plant has a different genetic makeup than the rest of it. I have read of people saving seed separately from sports so it is worth a shot to see what happens, or you can try vegetatively propagating the sport.
Diablo Ninebark being a 'bad sport' and growing a branch that has reverted to its usual green colour. Actually I like all colours of this native shrub even the original.
Rules are for other people?
Okay, if you really only have a very small population of plant X and really want to save seeds then you need to know plant X's reproductive style. Is it an outbreeder or an inbreeder? How is it pollinated? Is it self incompatible? Peas pollinate themselves and are inbreeders so they don't suffer from inbreeding depression. So you can save from one plant and still get vigorous offspring. BUT, it is always better to save from more plants to take advantage of hidden genetic gems which would otherwise be lost.
Make a Seed Bouquet. If you do, I promise to send someone a cool gardening book of my choice once I unpack stuff at my new house OR an assortment of seeds - unlabelled, like a grab bag... alright, I'll even label them.
After receiving entries, I'll choose at random for the winner but there may be honorary prizes for people who try hard. (If you are the only entrant, you are sure to win - incentive eh?) Show your seeds!