Cactus flower?
My wife saw this plant at a friend's house and liked the way its long leaves grow from other leaves. Our friend gave her a leaf, and the plant developed well. What we didn't know was that it blooms - it happened for the first time 2 years later. The flowers are very delicate and last only for a couple of days. I searched on the Web and found that it's a cactacea, Lepismium houlletianum, also known as Rhipsalis houlletiana and a few other names. I couldn't find a common name, though - probably because it's not a very common house plant...