The Gongora orchid genus is a really neat type of orchids, related to Stanhopea. They have nice, strong fragrances, often of cinnamon, allspice, or nutmeg. The flower stems hang over the pot's edge and the flowers point downwards. They can adapt to a wide variety of lighting conditions and a relatively large temperature range, but like a lot of water.
Cycnoches orchids have unisexual flowers, meaning they have separate male and female flowers which look different (usually just one of the two types of orchid flowers each time it blooms). The flowers are usually make a very dramatic display. After flowering, the leaves drop off and it enters a dry rest; don't water until it starts to grow again or it will rot.
Cymbidium carry tall stems with many flowers that have a more typical orchid shape. They are easily identified by their grassy leaves, and they readily form large clumps. Most common are the cool-flowering types, which need to experience a cooler winter (nights in the 40s for some time in the fall) in order to initiate flowering. Once the flowers open, they can last for up to two months or more, especially in a cool environment. These are very showy and rewarding plants, and a plant in a six-inch pot can carry three stems with 15 or more flowers each, depending on the type.