No doubt, everybody's idea of what are 'essential' herbs is going to be different. I couldn't do without mint, of which I have several kinds. Spearmint is the one I use the most. Of course, I have a herb-only garden, so I think they are all essential! I particularly like having fresh turmeric, ginger, lemongrass and galangal readily available, and I wouldn't be without lavender or aloe vera, either. Surely a herb garden isn't a herb garden without some parsley in it?! The elder tree is one I really like to have for both culinary and medicinal uses. Feverfew, agrimony, nasturtium, chillies, kafir lime, lemon verbena, tarragon - the list goes on. I used to have literally hundreds of herbs, but now that I have only a tiny little garden, I've had to limit myself to the ones I use the most. Although stevia and heliotrope and caraway and a few others are more for the novelty value and I can't bring myself to part with them!

Hmm, I find it hard to define 'essential' as there are some I don't use much but like to have around anyway. Its in very rough order of usefulness with the most essential to me at the top. I agree you've got to include parsley though, unless you hate it.

Parsley
Basil
Rosemary
Mint (for cooking and tea)
Lemon balm (for tea)
Oregano
Bay laurel
Garlic chives
Fennel, bronze
Sage, purple

The only herb in my garden that I could bring myself to leave off this list was hyssop - it's ok as a drought-resistant little shrub, but I don't cook with it or use it for anything else.

Like daisy I also grow chillies though she probably has a better climate for it, and nasturtium for occasional additions to salad. I would count coriander (cilantro to you) as essential if only the stuff would grow well for me.

I get the most use out of Lemon Verbena and all the various Mints from my garden. Second place would be Basil and Rosemary. Third would be garlic.

Parsley
Basil
Thyme
Oregano
Rosemary
Mint
Chives
Sage
Dill
Caraway

Also:
Garlic
hot peppers
Shallots

I'd suggest that you grow what you use in cooking to get started. Many herbs also make lovely garden plants, but that's another issue.... it all depends on how much garden space you have.

Thyme
Tarragon
Arnica
Calendula
Chamomile
Garlic
Sage
Rosemary
Elderberry
But, how can you leave out things like borage and salad burnet and motherwort and comfrey and grindelia and black cohosh and chives and, and...I grow over 250 herbs and feel they are all essential. Hawthorne, mugwort, tansy, echinacea. Roses! Lemon Balm. Lemon thyme. Help, I can't stop!

I would definitely add summer and winter savory and chervil to what everyone else is suggesting.

Sweet marjoram is another must.

After planting a huge variety of herbs in my first herb garden last year, I'm going with what I used most fresh and harvested for drying:

Basil (essential for great pesto)
Lavender (infusing simple syrup for your tea will make you glad you grew this one)
Rosemary (couldn't live without this one)
Chives
Sweet Marjoram (unbelievable perfumy fragrance)
Italian Parsley
Oregano
Mint (my fav, Kentucky Colonel's Mint, a strong spearmint)
Sage
Cilantro
Savory
Thyme (love its lemon freshness!)

Of course, cilantro and parsley can be purchased in large quantities fresh in your grocery store all year around. But there's something quite satisfying about having it in your own garden and clipping your own.
And the grocery stores have those little packages of rosemary, thyme, basil....ugh! Why bother? I see them and chuckle.

Of course, cilantro and parsley can be purchased in large quantities fresh in your grocery store all year around. But there's something quite satisfying about having it in your own garden and clipping your own.
And the grocery stores have those little packages of rosemary, thyme, basil....ugh! Why bother? I see them and chuckle.

I still have had problems with cilantro! It's supposedly a cold weather crop?
The only other one I'm having troubles with is arugula.
any suggestions?

Where I come from, arugula is called Rocket. And with good reason. Like coriander, it'll bolt to seed in the blink of an eye. Best thing to do is plant successive crops, and let each on self-seed. The babies will come up at (hopefully) different times, so you've always got leaves on hand. You can slow things up a teensy bit by removing every flower as it appears. Or grow them both only in winter!