The Aporocactus flagelliformis (rat tail cactus, rat's tail cactus) has thin weak stems (usually about a half inch in diameter) that can grow five feet long and hang down over the sides of its pot.
Aporocactus flagelliformis. See more pictures of cacti.
The rat tail cactus needs bright light and coarse heavy soil with excellent drainage. Drench and let dry, but water more sparingly during the winter. Air that is too dry can encourage red spider; air that is too moist can encourage rot.
In winter, keep the plants cold and dry to encourage blooming. In Mexico they grow at high altitudes where the night temperatures are very brisk. In rural areas the dried flowers are used medicinally. They are often planted in the open end of a cow's horn, making an interesting decoration.
This is an old-timer which is probably more often acquired as a cutting from a friend than through purchase.
Caring for your cactus: