According to Bras and Bras, there are ten types of bras:
Bandeau Bras
This bra is constructed of a strapless elastic band of fabric. It sometimes has a thin halter strap. The bandeau style offers very little separation or support.
Contour Cup Bras
The cups in this bra maintain their shape due to an underwire, fiberfill or foam which is molded into a specific shape. This bra can add a smooth shape and eliminate nipple bumps (great under knits) and is excellent for women with different sized breasts.
Demi Cup Bras
A demi cup bra covers less of your breast than a full cup bra. Generally, the cup stops about one inch above the nipple thus reducing the amount of support this style offers. Women with above average sized breasts may find that they are spilling out of this bra.
Full Cup Bra
Your basic, everyday bra. The cup covers most of your breast and offers a good amount of support.
Mastectomy Bras
This bra is intended for women who have lost one or both breasts in mastectomy treatment. A mastectomy bra is structured such that a prosthesis can inserted into the bra and held in place.
Minimizer Bras
Minimizer bras compress and redistribute the breast tissue towards your side and underarm, leaving the appearance of a one or two size reduction in cup size. Some women find the compression to be uncomfortable.
Molded Cup Bras
The cup in this bra is seamless and has a preformed, molded cup. They can be made of a soft or rigid material. Molded cup bras are frequently worn under t-shirts and knits since they provide a smooth appearance.
Push-up Bras
This style is worn to achieve cleavage. The bra cups are designed to lift the breasts and are angled, forcing the breasts inward creating cleavage. Some styles also have a removable, elliptical-shaped pad which, when placed at the bottom of the cup, pushes the breast inward and upward making them look larger.
Racerback Bra
The name for this style comes from the unique configuration of its straps. Racerback bras have straps that join in the center of the back either in a T-back or Y-back depending on the exact configuration. This style is often used in sports bras since it provides a larger range of motion.
Seamed Cup Bra
The cup in this bra is made of two or three sections. The seamed cups provide more support than a molded cup. The seams in the cups may be visible under many fabrics including thin knits.
Soft Cup Bras
Soft cup bras do not have any wires around the cup. This style is usually a molded cup and is sometimes padded or lined.
Sports Bras
If you are active, you need a sports bra. Sports bras are designed to maximize the support of the breast and minimize the bounce. Bouncing breasts aren't just a nuisance, they can cause long-term damage. Sports bras come with or without an underwire.
More information on selecting a sports bra.
Underwire Bras
As the name implies, a wire is sewn under each cup of the bra to provide extra support. The wire is generally made out of metal or some hard plastic. Women with large breasts usually feel that need the enhanced structure this bra offers. Either you love them or you hate them or just need them.