There are hundreds of varieties of plants that can be grown successfully indoors. The key to success is to match the plant to the conditions, and by far, the most important factor is the amount of light that will be available to the plant.
Light can be either natural or artifical.
Natural light has the advantage of being a gift from nature and provides a wide spectrum of light, making it the most suitable for foliage and flowering. Artificial light is more expensive, but the advantage is that you can put it where you want it. Generally, plants require either sunlight, bright light, medium light or low light. Unfortunately, these terms aren't always used. Looking through a few sources you will find light levels called shady, filtered, intense, indirect, or reflected.