Herbs are annuals: basil, coriander, dill, arugula,borage, chervil, fenugreek, nasturtiums, roselle, perilla, epazote, sesame
Biennials which will grow the first year and flower in the second: parsley, caraway, green onions
or perennials like: mint, rosemary, bay leaves, Mexican tarragon, sage, lemon grass, garden chives, garlic chives, oregano, thyme, lavender, ginger (it does die back to the ground every year), turmeric, horseradish, scented geraniums, echinacea, verbena, lemon balm, bee balm, pineapple sage, and hot peppers.
There are many others that I still have not mentioned. Most of the shrubby herbs and spice trees will be perennial in milder zones. Others will require winter protection in colder zones. Herbs are a very diverse group.
Invasive herbs like the mints, lemon balm, artemesia are best kept contained in pots and they do need to be monitored to keep them from choking themselves out or escaping. The herbs that are not hardy in your area should probably also be kept in pots so they can be sheltered for the winter.
Even among the herbs there is a wide range of soil preferences and light requirements. Most want to be in the sun, but the grey leaved herbs require much less water than the mints and their relatives (they all have square stems), which prefer a moist rich soil. Rosemary, and lavender are two herbs that I know that prefer well drained soils that are not too rich.
Some herbs like dill, borage, perilla, fenugreek, cilantro, caraway, flax seed, and nasturtiums will only grow best for part of the year for me.
Many of the herbs will reseed and come back, that is what happens for me with lemon basil, thai basil, sesame, epazote, and perilla. The fennel would probably also reseed, but I collect the seeds and pull the fennel usually before that happens. Fennel can be a perennial, but I grow finocchio fennel for the bulbs so I start with new ones every year.
Spearmint, plantain, and gotu kola are weeds in my garden. The gotu kola and plantain blew over from the medicinal herb garden, the sesame from the Children's garden, and the mint escaped .
Happy gardening in Hawaii. Gardens are where people grow.