A traditional food is Nopalitos - the pads of Prickly Pear Cactus (Opuntia sp.) that are prepared by removing the spines and then steaming. They are actually quite good and are probably available in a can or jar in the Mexican food section of your grocery store - and maybe even fresh if you are lucky. They are a very common ingredient in meals usually served as a side dish. They taste a lot like string beans.
The attached photos are of a vegetable vendor in the old city market. He was nice enough to demonstrate to us how to prepare a cactus pad without skewering ourselves.