The ones that I have are Christmas cacti by the way. There's also Easter cacti, which have flowers that look a bit different and flower around Easter instead of Christmas. These plants are very strong; they've managed to survive on top of my heating, where it gets really hot and dry. Another reason why I love them is that they are very simple to propagate. You just tear one of their parts/leaves off and let them dry for a couple of days, like this:
Then you plant them in soil, I used normal potting soil, and keep it a bit moist but not too wet. At first, the leaves will wrinkle a bit, as if they're drying out and dying. But no worries, that's normal. After a few weeks, they'll get roots and start looking healthy again. And before too long, they'll start growing new leaves of their own.