Rambunctious Self-Seeders,Creepers & Tubers in the Vegetable Garden

There are a number of edible plants that oblige us with their presence in a robust and adventurous way.
Many of them are herbs, both medicinal and culinary, like dill and mints. Edible flowers are another large group, including: viola, pansy and calendula.
Some folks prefer a more controlled environment, but I love the rascals that pop up on their own because I didn't have to expend any energy planting them or money to buy them. This kind of indulgent plant-parenting does require a few rules or the garden will have only these hardy characters.
I call this "Subtractive Gardening". It's very simple: if you like the plant, leave them where you want them and remove them where you do not (or transplant to a preferred location). Sometimes transplanting doesn't work as well as letting the seeds choose their own places, but most often they happily settle in elsewhere.
Self-seeders are usually annual plants that grow from seed to bloom to setting new seed in one growing season. Stout annual seeders include: arugula, borage, calendula*, dill, feverfew*, catnip*, epizote*, fennel*, lemon balm, nasturtium*, sunflower, viola and pansy. Those with an asterisk, are the ones to keep an eye on, especially nasturtiums and calendulas. These two can easily take over the spring plantings with their extreme vigor. On a weekly basis, I  pull the majority of seedlings. If I didn't they would quickly out-compete the fussier garden vegetables.
Then there are the creepers. These are usually perennial plants which come back from their roots year after year. While many perennial garden plants keep to their own tight root ball, others crawl over and under the surface of the soil with their exploratory roots.
All of the mints fit this category and my strategy is to put them in a large bed of their own where they can compete with each other. I keep them out of the rest of the garden entirely.
Two years ago I had to dig out a bed of apple mint that in just two or three years had grown from one 2 gal pot stuck in the ground, to a circular plantation 10' in diameter. It no longer is allowed anywhere in the garden. Apple mint roots that occasionally show up, go into the garbage. I can't risk having them coming back in the compost bin or weed piles.
A few biennials (plants that survive the winter and finish their life-span the following summer) also reseed. There are a number of vegetables in this group: carrots, parsley, kale, broccoli, lambs quarters, spinach, beets and swiss chard. I don't count on these to reliably come back, but I do honor the tenacity of those that do by letting a few of them share space throughout the garden. I still order fresh seed from nurseries to hedge my bets.
Two tuberous vegetables are loved and/or feared by seasoned gardeners and they are: Jerusalem artichokes (sun roots) and potatoes.
Sunchokes are sunflower family plants which I have praised in a previous posting, however, do plant them in an out-of-the-way spot and don't throw their tubers willy-nilly about the garden. Potatoes leave tiny potatolets in the previous year's potato patch, which sprout and become new potato plants under, in and around everything else you try to grow there in the years following. Sometimes they can grow between things where they are, or they can be transplanted when small to their own bed. Some people say that potatoes lose vigor after years of doing this without bringing in new tubers. In the permaculture garden, so far, so good.
Little seedling that pop up all over the garden are like little presents or little scoundrels, uniquely leveraged in every beholders eyes. Choose your friends wisely and chase away your personal villains. If I were you, I'd think twice or thrice before planting calendulas, catnip or fennel unless you are fond of weeding or committed to cutting the flowering heads before they turn to seed.
Here's to the happy little rogues!