A wide selection of vegetable seeds can be saved for future use.
Many vegetable seeds can be saved for sowing the next year. In fact many of the prized specimens that win vegetable shows are from seeds which have been selected and saved by the grower. In particular, giant leeks are normally the case of own-saved seeds.
Seeds that you should not attempt to save, are those from plants which we F1 hybrids. These will not come true to type, and in many cases there will be inferior seedlings as a result.
The main reason that self saved vegetable seeds are a failure the following year, is because of poor storage conditions of the seeds.
Seeds should not be stored in warm, moist conditions. If so they will deteriorate quickly and soon become non-viable. Saved seed should be stored in dry cool conditions - preferably in an airtight container - after firstly being dried off and ripened properly.
If you have a lot of saved seed, then it is a good idea to put them in a large airtight storage box - in their own individual container. You should place some moisture absorbing silicon crystals in the large box to help mop up the surplus moisture. Store in a cool dry place - maybe a garage or shaded shed, but not too near the roof area, which can soon warm up in any winter sun. Bear in mind also that heat rises, so the higher up your stored seeds, the warmer they will be!
Make sure that the seed you want to store has been properly ripened - ideally just falling from the pod! Spread them out on a sheet of paper in sunlight for a few hours to finish the job properly. Make sure that the sheet is anchored down, and that it is not an area where fine seed will blow away. Bear in mind that a nice crop of drying seeds will be a big attraction for your local bird population!