If you go into any Korean supermarket, you'll find several staples sold in an overwhelming array: kimchi, anchovies, pickled garlic, and a variety of rice cakes that are not available at Chinese or Japanese stores. At a Chinese store, on the other hand, you might find a few packages of presliced rice cakes (nian gao, in Chinese) for use in stir-fry dishes, but even a small Korean supermarket will carry an impressive range of rice cakes (dok, in Korean).
What is a rice cake? Glutinous rice is pounded to a gluey, sticky mass, which is then formed into a variety of different shapes and sizes. Shape-wise, there are chubby and skinny, tall and short, round and oblong. Color-wise, they can be pale (made with white glutinous flour) or tan (made with brown rice). You'll find freshly cooked rice cakes, most frequently in cylindrical form, sold at some stores, though all Korean markets will carry refrigerated, pre-packaged rice cakes that must be boiled before use.
Though all rice cakes taste like pounded rice (even the ones made with brown rice vary little in their taste), the specific shape dramatically affects the texture. Thin slices are significantly less chewy than large, cylindrical rice cakes that are genuinely toothsome in the degree of their chewiness.
Here is one instance where there's truly no "better" shape—each is well-suited to its purpose. A thin rice cake quickly soaks in flavor and is good for a stir-fried dish with slices of meat or vegetables. A thicker, rounder rice cake can be toasted in a cast iron pan or even charred over a grill, and still stay pleasantly chewy and soft in the center.
In Korean cooking, rice cakes are a mainstay of kimchi stews, for which almost any shape and size of rice cake will flourish. Sliced rice cakes need significantly less time to cook than the more thickly shaped sticks, but those chubby cylinders of pounded rice, you should know, char wonderfully when lined at the bottom of a clay pot.
Asking the question, what should I cook along with the rice cake? may half-miss the point—it's like asking an Italian what garnishes should accompany a freshly made plate of pasta. The pasta, valued for its specific textural qualities, is the primary draw of the dish, just like the rice cake is the main attraction. (This is not to say, of course, that a rice cake wouldn't make a superb filler for just about any stew you're contemplating.)
Koreans relish the chewy texture of the rice cake with very little garnish and side ingredients. The classic preparation of dok boki is to boil the cylindrically shaped cakes and eat them coated in a red sauce of chili paste, fermented bean paste, soy sauce, and sugar, topped liberally with sesame seeds. You can follow the traditional route and boil your rice cakes in water or you can pan-fry them with a little bit of oil in a skillet. Or, char the cakes under the broiler until the surface is crackly and the inside is gooey and warm. The bibim sauce—a tasty balance of sweet, savory, and spicy—is a wonderful dressing for the chewy cakes.
Of course, once you're hooked on the texture, you'll find all kinds of ways to incorporate the cakes into your diet. In the mornings I've been known to dip broiled rice cakes in a mixture of peanut and honey with my coffee; in the evenings, I might fry one or two in bacon fat or olive oil to accompany my meat and vegetables. However you decide to use them, freeze whatever you don't use. The smaller, thinner varieties can be tossed directly into the soup pot from the freezer, making them a quick addition to your late-night kimchi soups.