By now I think it's reasonably common knowledge that curry powder is a British invention, not an Indian one. Indian cooking is no more summed up by that blend of turmeric, cumin, and black pepper than American cuisine is by ketchup and cheddar cheese. But there is a spice called curry—even by Indians!—whose singular aroma and flavor herald Indian cooking more than almost anything else. I'm talking about curry leaves, the nigh-magical herb essential to much of South Indian cooking.
Curry leaf doesn't define regional cuisine in the way spices like paprika or cumin do. It's not even a dominant flavor in most dishes; instead it takes a backseat role, similar to bay leaves in Western cooking. But there's nothing mild about curry leaves, and dishes made without them lack a the verve and depth of flavor that makes this style of cooking so damn good.
Curry leaves taste a bit like asafoetida, another essential element of cooking in regions like Tamil Nadu and Kerala. But it also has a more herbal feel, slightly like basil or kaffir lime. The aroma is also similar to asafoetida or sharp feta cheese, by which I mean to say it has that ultra-savory stinky feet quality so appealing in strong-flavored foods. (Hey, people pay thousands of dollars for truffles; curry leaves by comparison are a bargain.)
Confusingly, they don't taste at all like the curry us Westerners are used to, which is mostly the North Indian variety (heavy in Persian and Arab influences), rich with cumin, cinnamon, cardamom, tomatoes, nuts, and cream. South Indian "curries," a category that's only slightly more narrow than "liquid-based food," are leaner and rely more heavily on legumes and vegetables. These dishes, usually vegetarian lentil-based pulses or sambars (thin soups used for dipping fried foods and savory pancakes) are generously spiced with asafoetida, mustard seed, curry leaves, and others. Their flavor is unlike any spice blend on Earth, aromatic to the extreme, and, if you're like me, highly addictive. Curry leaves are such an integral component of these dishes that the Tamil word for them is kariveppilai, which literally means "the leaf used to make curry."
Curry leaves are typically bruised in the hand, then fried in hot fat (usually oil, though sometimes clarified butter, known in India as ghee) with other spices at the start of a dish, to flavor the fat and the vegetables to come. They can turn black in this process, which is just fine. Like with sage leaves, you can remove them once they crisp up and use them as a garnish, or just leave them in through cooking. Their flavor mellows as they cook, but remains distinct even after hours of stewing. There are no hard and fast rules here, but if you start a dish with a blend of mustard seeds, asafoetida, curry leaves, and dried chiles, chances are you're going to happen on something delicious.
I most frequently used curry leaves in dal, a stewed lentil dish that rivals chicken soup as Supreme Comfort Food and meat-and-cheese laden omelets as Supreme Hangover Food. They also go into my rasam, which I'll sip on its own or use as a dipping sauce for fritters. But it's also used in rice dishes, vegetable sautés, and vada, spiced fried snacks made with chickpea flour.
You can find curry leaves at well-stocked Indian groceries, either with the herbs or in refrigerators. They last reasonably long—for an herb—in the fridge, but I typically store them wrapped very tightly in plastic in the freezer. They will blacken with time, which can be stalled with airtight wrapping, but the flavor will dissipate over time. Stored optimally, you can get four to six weeks out of your curry leaves before you have to head back to the market. Which shouldn't be a problem. Once you start cooking this type of food, you may find it hard to stop.