I currently grow Rosemary on my windowsill. What are some other herbs and spices that are easy to grow (and useful)? I live in South Carolina, USA. Plants are indoors = 65-75F all year.
Herbs are generally very easy to grow, as long as you don't forget to water them regularly and provide a well drained environment with sunlight at least 8 hours of the day. What you should grow largely depends on your culinary tastes (and what's expensive in your area).
I must stress one point though: only plant herbs that you will use regularly. The reason is that the flavorful herbs as we know it are the young leaves of the plant. At this stage in the plant's life, its sole purpose is to grow and as such, the leaves are wider, lush, tender and rich in the aromatic stuff that we love. Once plants reach maturity, it's focus is to reproduce and die. So the new sets of leaves it produces are a lot thinner and in general, less aromatic (sometimes gets bitter). No other herb illustrates this better than cilantro. If you've grown cilantro and let it take its own course, you'll know what I'm talking about. This also happened to me with dill and thyme.
So if you use these regularly, you'll be automatically trimming the plant, keeping it forever young. If you must plant something that you don't use often (or if you find that your plant produces more than you need), you must trim them often (give the excess to a friend) and not let them flower (pinch the flowers). Speaking of pinching flowers, one herb for which this is very important is basil. This was addressed in a different question on the best conditions for growing basil
Source: Personal experience from growing several herbs (cilantro, basil, mint, dill, marjoram, parsley, sage, rosemary and thyme). I also found this very helpful website where they list the requirements (light/spacing), how to grow them (from seed/plants/cuttings) and general tips. Do give it a read if you're interested in the requirements for a particular plant.
My kitchen window once held basil, parsley, cilantro, and chives. All but the chives apparently need more light than that window permits, but even so were easy to care for and survived some neglect. The chives have been incredibly easy to grow and quite useful in cooking.
I also have an aloe vera plant that happily exists with no particular work on my part beyond a bit of water now and then. The gel from a broken-off piece of the plant can be used to soothe wounds or burns. (I don't know what, if any, healing properties it might have, however.)
I picked these plants because I already found them to be useful in cooking and wondered if they would be easy to grow. My experience suggests that herbs in general are simple to care for and there's no reason not to take a risk on something that sounds interesting to you.
In any case, I recommend using small pots to make it easier to move your plants in case the windowsill turns out to be a sub-optimal location.