This is a cholla (pronounced choy-ya) cactus or
Cylindropuntia fulgida. The long strands hanging down are cholla fruit. There is a different species of cholla just to the right of the big cactus, that is known as a pencil cholla or
Cylindropuntia arbuscula (Engelm.) F.M. Knuth. In the background to the left, hidden by a bush is a prickly pear cactus or
Opuntia. I can't quite see enough of the Opuntia to tell which species it is but it is probably the
Opuntia engelmannii or Englemann Prickly Pear. If you look way in the back of this photo, you can see some saguaro cactus or
Carnegiea gigantea. You might have to click on the photo to see the saguaro. Right behind the stem of the large cholla, you can see a Hedgehog Cactus or
Echinocereus engelmannii. There are also some
Cylindropuntia bigelovii or teddy bear cholla in the background. Everything out in the desert and everywhere else probably has its own name. It makes the world seem like home when you know the names of some of the plants.