At my house, we've largely given up on growing "greens" because there are so many edible and tasty weeds that come up all on their own without any help. Our mainstays are chickweed, broad-leaf plantain, violet, dandelion, and lamb's quarters but there are a ton of others (amaranth, galinsoga, dock, burdock...) -- and it's worth noting that many of these were actually brought over by European colonists or were cultivated by Native Americans. They're just thought of as weeds today, but they make a fine salad.

Many of these would be bad to eat in large amounts, but humans are "generalists" -- we're built to eat smaller amounts of a variety of things together. The same is true for a number of our modern cultivated crops; off the top of my head the things in the mustard, spinach, and carrot families are mildly toxic, but we eat moderate amounts of each, so it works out.