There are a lot of complex and difficult things to grow that successful gardeners are rightly proud of when they produce. The items I want to bring forward are things that are easy to garden, that require little or no effort to grow, and that reproduce themselves easily or hang around for a long time. Since I live in zone 5/6 (right near the line, so it changes depending upon the map you look at) that is what I know, so I will focus on there. Some of this will carry over to other zones, some won't.
- If you have the room, you just can't beat something that, once planted and matured, will produce yearly bushels of food for more than a lifetime. Annual pruning will maximize production, but even neglected trees produce more food than can be consumed at harvest time. Preserve or trade the surplus. Look around your area for what is growing in neighbors yards and nearby farms.
- Usually the quickest producing thing in a vegetable garden. The secret is to let some of the biggest ones go to seed. They will reseed themselves with no effort on your part producing you free radishes every year after that.
- They quickly produce flowers that will bring in the bees.
- The seed pods are edible and taste like radish when young.
- A bonus is that the plant eating bugs in this area love the radish plant leaves to the extent that my radish plants are full of holes, but the beans, peas, tomato, lettuce, etc are left alone.
- The plant everyone loves to hate. If you let a few go to seed you will get a second crop in the fall, and next year there will be more.
- A great herb that easily reseeds itself without any help, just let a few plants mature completely.
- The honeybees around here love this stuff: hundreds of small purple flowers. Let it seed itself, as it grows the small, young leaves have a cucumber like flavor. As the plants get bigger, chop and drop the plants in your way for instant composting mulch. Let only a couple plants mature in an out-of-the-way spot and you are sure to have more next year.
- As a caution, this can become a weed if you let too many of them mature. Just cut the stem at ground level (hoe, machete, clippers whatever works), let the plant lie where it falls to help suppress weeds.
- Oregano and chives will come back every year, rather than reseeding themselves, so plant them in a place where you won't disturb their roots.
- New this year I tried rosemary and thyme, so we'll see how those go.
- Not much to say there, it comes back every year and you can cut off root sections to replant elsewhere to have more plants.
- Strawberries and raspberries are doing well. Blackberries, blueberries, etc are also said to do well in this climate, but I personally don't have any... yet.
This, of course, is not an exhaustive list of things that stay or reseed themselves, but it is what I have in my garden that I don't need to plant ever again, but still reap produce yearly for only the cost of summer watering. I encourage you to try some of these things, or, just let a few of your garden plants go to seed and see if will come back next year.