This is New England's only native cactus. It's listed as "threatened" in all of New England, except for Vermont, where it's listed as "extinct". It's native habitat is "barren mountain ridges, high beach dunes, stone walls". It has very showy flowers, and the entire plant is eaten in Central America. The pads are called "nopales", and are cooked a lot like squash. The fruits are "pears", and are mostly made into jam or jelly.
This specimen came from the Garden in the Woods in Framingham. Last year, when Waltham was resurfacing our sidewalks, we trimmmed it to keep it from attacking people walking by. If you have a place for it where people won't bump into it accidentally, you can take one of the potted plants and help an endangered species.
Note: Don't touch the plant. It's vicious. Use kitchen tongs and a sharp knife if you want to trim yours, or remove the clumps of spines, or pick the fruit. It's easy to find recipes online.