I grow basil, cilantro, oregano, and garlic chives. I have grown some others in the past, but I find I don't end up using them! Since I'm in an apartment with a covered balcony, my grow light space is at a premium. So I only grow the ones I use a lot, and that are worth it to me (the ones that are significantly better fresh than dried).
But if I had more space I would add more basil varieties (I have two by accident--the seed packet contained two varieties), and additional cilantro plants, so I always have a mature one. Also another variety or two of oregano, plus thyme and maybe parsley. I like the idea of having rosemary, but I rarely use it.
I also grow some greens and vegetables which grow just as quickly and easily as herbs: Spinach, leaf lettuce, butterhead lettuce, radishes, baby bok choy, and now I'm trying some fingerling carrots.