I've been growing parsley, mint, sage and garlic chives next to a window in winter for many years, but not basil or oregano as you suggested. I'll have to give them a try.

I once tried overwintering rosemary indoors. The plant survived one winter but went downhill the next summer.

You didn't mention cilantro or tarragon. Have you ever raised that indoors in the winter?

Thank you, Johnathan, for writing this (albeit 3 years ago)! I've been kicking around the idea of starting an indoor herb garden, since I'm kind of an avid cook and even dried herbs in a bag are getting pricey these days! I'm sad to read dill is only an annual, though: that's become a favorite for use on fish, and we'd likely go through even a 4' tall plant as fast as I can catch fish and finely chop sprigs of dill! haha

It's good to know I'm not the only one that can't keep a rosemary alive, Don! I tried my best for about half a season, but that was all she wrote. In my case, I think it was just over-watering (I didn't realize it was a Mediterranean plant-- all I saw was another evergreen at the time! O_O).

Based on my research, which I'm sure you've already done as well by this point, growing cilantro indoors is about the same as most others: it wants 4-5 hours of sun per day, water when soil is dry to the touch, etc. I looked up tarragon, but to my novice eyes, I can't tell what's what there and there are some odd-looking requirements (some sort of dilution with fish fertilizer?), so I won't purport to have any knowledge on that.