Thus far I've grown thyme and mint, both tasty plants which are as practical as they are fragrant.
Mint is a nice plant which is insanely easy to grow, it smells nice and can be used in cookery.
Medicinal Use
Mint was originally used as a medicinal herb to treat stomach ache and chest pains, and it is commonly used in the form of tea as a home remedy to help alleviate stomach pain. It also doubles as an antipruritic - which means it stops itching.
Notes
While mint can tolerate direct sun it prefers the shade, and it shouldn't get over-watered. If the top of the soil feels moist, or damp, then it is fine.
Thyme is another nice plant which is insanely easy to grow, it smells nice and can be used in cookery.
Medicinal Use
The main component of thyme is thymol, which is a natural antiseptic.
Notes
The plant likes the sun, but will cope without it. Watering is basically the same as for mint, but if anything less water is required.
My thyme grew from seeds to 10cm in a couple of weeks, although I've heard people say you shouldn't harvest for the first year I'm doing so already..