A true annual grows, flowers, sets seed, and dies within one year. Sometimes a biennial herb acts like an annual and vise versa. Some annual herbs are basil, marjoram, summer savory, dill, calendula, anise, chervil, and cilantro. Cilantro usually refers to the leaves of Coriandrum sativum while coriander usually refers to the seeds of the same plant. Calendula, cilantro, and dill are the most likely to reseed if you don’t cut your plants back until the seed has dropped. I have never heard of basil reseeding.
Biennials grow leaves the first year and flower, set seed, and die the second year. Borage, parsley, clary sage, and angelica fit this category. Sometimes borage is an annual. Parsley leaves can be harvested for a short time during the second year of growth. I let my parsley reseed the second year so it plants itself for the following year.
Perennials live for two or more years before dying. Some perennials live many years. There are shrub like perennials such as sage, lavender, thyme, and hyssop which do not die down to the ground for the winter. Other perennials including lovage, fennel, and sorrel grow back from the ground each spring. It is important to know which is which because it most cases you do not want to cut the shrubby herbs to the ground.
Some perennials listed above may be a tender perennial in your climate. This could be due to winter temperatures or it could be due to other factors including soil moisture. Sage, lavender, and French tarragon are perennials in my dry, zone 6 garden. Even those who have the same climate zone may not be able to grow them outdoors because the soil stays too wet. The variety also makes a difference in whether something is a perennial in your climate zone. Many lavenders survive in my zone but Lavandula stoechas is one that will not survive winters in my area. ‘Arp’ rosemary usually survives the winter in my garden but once every few years there is a winter that kills it off. Garlic is a perennial but is usually harvested within one year for the cloves which will reproduce but get smaller over time if not harvested.
Perennial herbs in my zone 6 garden include: sage, lavender (most), oregano (most varieties), thyme, winter savory, ‘Arp’ rosemary, French tarragon, fennel, lovage, mint (most varieties), Roman chamomile, comfrey, feverfew, Bee balm or Monarda (most – one is an annual), lemon balm, catnip, lady’s mantle, lungwort, anise hyssop, hyssop, sorrel, French sorrel, saffron, chives, garlic chives, germander, costmary, and yarrow.
Tender perennials can live many years outdoors in your climate or can be grown as a houseplant in colder climates. In my climate zone some tender perennials are lemon verbena, scented geraniums, stevia, bay, lemongrass, ginger, and turmeric so I grow them indoors or move them inside before the temperatures drop.
If you have a patio or deck you can still grow some of the above plants outdoors. If not, you can grow some of them as houseplants.
For other ideas for edible and medicinal plants you can grow in your landscape or indoors check my post Edible Plants for Your Landscape