Ask Mr. Smarty Plants

Unfortunately, "cactus" is much too wide a term for an accurate answer. You didn't say if your cactus was a house plant or growing outside. In New York, that, alone could answer the question. If it's outside, it probably can't survive the cold temperatures. Because of the heat generated by a large city, New York City has warmer zones than the rest of the state, but you are still in Zone 6a to 6b, which indicates a minimum average freezing temperature of -10 to -5 or -5 to 0 deg. F. Cacti, generally, are desert plants, and don't tolerate very low temperatures. On the other hand, if your plant is indoors and not getting lots of sunlight, it doesn't tolerate that well, either, for the same reason. It is way out of its native habitat. And if it is in a pot without adequate drainage, and/or you are watering it too much, it is probably suffering from that.

Just to demonstrate our point, see this Eduscapes website on Cactus  (Cactaceae).There you will see a number of pictures showing the variety of plants in that family. It further states that there are over 2,000 species that fall in that category.

Three of the genus members of the Cactaceae family:

Mammillaria Sample North American native: Mammillaria pottsii (rat-tail nipple cactus)

Opuntia Sample North American native: Opuntia engelmannii (cactus apple).

Melocactus  According to this USDA Plant Profile, this plant is native to Puerto Rico and the Virgin Islands, but not to continental North America, so it does not appear in our database.

Many plants not even closely related are mistakenly called cactus. We have listed some of these, with native examples and links to pictures.

Yucca Yucca faxoniana (Eve's needle)

Sotol Dasylirion leiophyllum (green sotol)

Nolina Nolina lindheimeriana (devil's shoestring)

Dudleya Dudleya cymosa (canyon liveforever)

Echeveria Echeveria strictiflora (desert savior)

Graptopetalum According to the USDA Plant Profile, this plant is native to Arizona and Texas, but does not appear in our Native Plant Database.

Ocotillo Fouquieria splendens (ocotillo)

So, we hope you understand why we probably can't diagnose your plant's problem, beyond the very broad range of temperature and light exposure.  If you have it indoors, and think the lack of drainage and sunlight might be the problem, we would suggest you repot it in a pot with cactus mixture potting soil (more sand, better-draining), very good drainage, and move it to a sunny window. Beyond that, you can try looking at all the pictures we have linked you to, and if you find one you think is your plant, Google on that plant's scientific name for information on it.