The plants of the Lily, Goosefoot, and Parsley families are self-sterile, cross-pollinating, or outbreeding. They will cross with other plants of their species. To save seeds from these plants you must allow only one variety in each species to flower at a time let multiple plants of one variety flower to ensure pollination.
In our dense urban environments, some crossing can occur with our neighbors' plants, but these plants will not cross over great distances. Many are rarely allowed to flower anyway.
Lily Family (Liliaceae)
chives, garlic, leeks, onions
They are biennial, which means they won't flower until the second year, after winter. Let the seeds dry on the plant. Collect. With bulbing varieties, replant bulb when it sprouts.
Amaranth Family (Amaranthaceae)
amaranth, beet, chard, lamb's quarters, orach, quinoa, spinach
Beet and Chard are the same species, so only let one variety flower at the same time.
Spinach is dioecious meaning each plant is either male or female, so let many plants flower at once for pollination. Let the seeds dry on the plant. Collect.
Carrot Family (Apiaceae)
carrot, celery, caraway, chervil, cilantro (coriander), dill, fennel, parsley, parsnip
Carrot, unfortunately, will cross with Queen Anne's Lace, so don't save carrot seeds if Queen Anne's Lace grows nearby. Many of this family are biennials, so flowering may not occur until the second year. Let the seeds dry on the plant. Collect.
Most Advanced of the Advanced Seeds
Most of these vegetables are outbreeding and pollinated by wind or insects. They are commonly found flowering in local neighborhoods, making isolation very difficult. Seeds that require hand pollination, tenting, and other methods to ensure varietal purity are labeled "advanced." These families will readily cross with unseen nearby plants and may create odd and possibly inedible varieties in one generation.
Mustard Family (Brassicaceae):
Asian greens, broccoli, Brussels sprouts, cabbage, cauliflower, collards, kale, kohlrabi, mustard, turnip.
Exceptions that are easy: Arugula, rutabaga
Gourd Family (Cucurbitaceae):
cucumbers, gourds, luffa, melons, pumpkin, summer squash (ex. zucchini), winter squash (ex. acorn).
Exceptions that are easy: Plant uncommon cucurbits like gourds, mixta squash, luffa. Hand pollinate to ensure purity with this family.
Grass Family (Poaceae):
barley, corn, kamut, millet, oats, sorghum, wheat.
Corn readily crosses with different, unseen varieties. It is unlikely that saved seeds will be like their parents.
Exceptions that are easy: Sorghum is easy to save because it does not cross. All other crops in this family are so uncommon in backyards that they are easy to save.