Long-grain white, brown or wild rice are common choices in chicken dishes, though the ideal type of rice for chicken and rice depends on the individual recipe. FoodNetwork.com offers a list of different recipes for chicken and rice, many of which use different types of rice.
Paula Deen's recipe for chicken and rice casserole includes dairy products including cheddar cheese and cream of celery soup. The recipe calls for long-grain wild rice. Martha Stewart's recipe uses brown rice in combination with savory vegetables including roasted peppers, tomatoes and garlic.
HalfBakedHarvest.com offers a recipe for an Asian-inspired chicken and rice dish with orange and cashews. This recipe uses cooked black rice.