Some plants propagate fairly vigorously without any human intervention:
- Strawberry, raspberries and mint send out runners to make new plants
- Blackberries, watercress will grow roots wherever a stem touches bare soil
- Winter purslane, nasturtium, watercress, borage, oregano, good king henry, wild rocket, red veined sorrel, calendula and cornflowers are insistent self seeders that I would recommend as edibles. All of these things I have planted once and, without any effort on my part, they come back year after year. They’re kind of in my personal order of edibility. I heartily recommend winter purslane to anyone who’ll listen. It tastes quite like lettuce, grows well in part shade and best of all does amazingly over winter. I’ve grown calendula and cornflowers and they keep coming back but I rarely eat them. They do add lovely colour to the garden though.
Winter purslane is a highly yummy self seeder 
One of the many wild rockets that has seeded all over my patio. 
Red veined sorrel has seeded it self at the bottom of a raised bed
Plenty of fruit will happily self-seed but you cannot guarantee how good this new plant’s fruit will taste. The same way children don’t pop out of their mothers as clones, plants that are grown from the seed of a tasty squash may not provide the same tasty squash as its parent. If you have the space and patience to see what you will get – the fruit could be amazing. However, you might find yourself nurturing a plant for 6 months in the case of a squash, or 4 years in the case of a cherry tree before you find out if it tastes any good. The new cross you may have created may not even have the disease resistance or be suitable for your conditions. Leafy greens and flowers, however, aren’t a worry. Because you’re not waiting for the fruit you’ll know soon enough if the new plants are worth leaving to grow.
Not a Horticulturist 