The most common cause of itching of the skin of the breast would be a contact dermatitis. Contact dermatitis is an inflammatory reaction of the skin caused usually be exposure to a chemical agent. Common offending agents would be a new soap, shampoo, or laundry detergent. If this is the case, then the best treatment is simply to discontinue using the offending agent. Topical over the counter anti-itch creams may also be of some use.
Fungal infections of the skin of the breast do occur, and they are not a serious medical problem. These are usually located in the skin underneath where the breasts hang down. If you have a crease of reddened and itchy or painful skin there, then this is almost certainly what is going on. In addition to good skin hygiene and keeping the skin dry, an over the counter anti fungal cream should clear the areas up.
Occasionally, itching of the skin is simply due to dryness, especially in winter months. Limiting exposure to hot showers and baths (which strip away the skins natural protective oils) and applying a good moisturizing lotion daily can help.
If these strategies do not work for you, then you should speak with your primary care doctor