At first that sounds ridiculous, right? An epiphytic cactus? But yes, really. Christmas, Thanksgiving, and Easter cacti are all epiphytic, as are the related orchid cacti (Epiphyllum) and mistletoe cacti (Rhipsalis).
And this one, Pfeiffera monacantha (formerly named Acanthorhipsalis monacantha). This one is native to Bolivia and Argentina, in the transitional zone between the Andes Mountains and the lowland forests.
It has very pretty little orange flowers, which are borne all along the edges of the stems in the spring. Mine is still a fairly young group of cuttings that I bought last fall, and I was not expecting it to bloom this year. Nice surprise!