Highly valued in South India and Sri Lanka, the leaves of the Curry tree, also known as Sweet Neem, are interesting; you can smell curry with the fresh leaves, especially when fried in oil. You can best use them with fish or coconut milk curries. They are best fresh, though their shelf life is short; you can also freeze them indefinitely (separate the leaves from the stems and remove any bad leaves); or you can dry them (to dry, put whole stalks with leaves between newspaper sheets and place in a warm area, like the top of a refrigerator), though this way they lose their flavour quickly.
Where do you find curry leaves? In specialty Indian stores, or certain Chinese supermarkets (which is where I found these). You can also sometimes find young curry tree plants for sale; you can grow them indoors and thus have a constant supply.
For a delicious recipe, try Eggs with Curry Leaves.