Hi elaerstelle - great question. There are a number of indoor plants that are wonderful and I'm sure everyone has their favorite. Here are a few:
Peace lily (Spathiphyllum) – handles lower light levels well and lovely blooms.
Spider plant (Chlorophytum comosum) - one of my favorites.
Pothos and Philodendrons – most of the varieties grown for indoor use grow downward like an ivy and make beautiful container plants.
ZZ plant (Zamioculcas zamiifolia) can survive in just about any setting. They are slow growers and have little demands for water and light, a very unique plant.
Aglaonema – Lots of colors and tough.
Aspidistra – the cast-iron plant. Tough and a favorite in Victorian times along with the Kentia palm.